Help with timing on transfers

Yes, doable, just. I have done this many times. It should take about 30 minutes, so 1 hour is the minimum I would book to give some safety.

• Problem 1: you say "I am totally unfamiliar with the London Underground", that implies you don't have Oyster Cards, so you will have to buy tickets from the ticket machine, which will delay you about 5-10 minutes, as you are "green". Make sure you have change.
• Problem 2: Find the correct Underground line at Paddington. See station plan here: http://www.nationalrail.co.uk/stations-and-destinations/stations-made-easy/london-paddington-station-plan The underground line you need ("Hammersmith and City") is not underground at Paddington, it is on the surface, same level as your arriving train. You need to go up onto the bridge which is level with the middle of your train (see plan), then across. Another way to loose time.

CONCLUSION: doable, but a bit stressed for a newbie.
Alternative 1: Get the next train to Edinburgh, there is a train every 30 minutes.
Alternative 2: (best option) Get a train by the shorter route from Bath to Edinburgh, via Bristol and Birmingham. by this route all your changes are in the same station AND it is quicker. For example:

08:55 depart Bath Spa, Bristol Temple Meads arrive 09:10
09:30 depart Bristol Temple Meads, Edinburgh arrive 16:06

Plus other options through the day.

Just take a taxi. Easier and you have adequate time. You can take the tube but you will be lugging luggage up and down stairs with a bit of hike to get from one station to another. Especially if you have medium size luggage.

I'm not too sure about a taxi mid-day midweek. Euston Road can be difficult. The Tube will be a bit difficult with luggage but reliable. Both Circle and Hammersmith & City connect Paddington and Kings Cross St Pancras.

The timing problem is tight. Hope your train from Bath is on time.

Public transport will be much quicker than a taxi. Take the Hammersmith and City or Circle line on the underground which should take 12 minutes plus getting down then up from platform level plus waiting for a train, so say 20 minutes. Your trip should be possible unless your Bath train is late.

What kind of tickets do you hold? One ticket for the whole journey or more than one, advances etc?

This can be important if you want to be covered in case of delay to be able to use a different train from Kings Cross.

Marco, we bought our ticket from London to Edinburgh in advance to get the great deal. Now I'm looking at getting from Bath to London, so will be two separate tickets.

Based on everyone's responses, I have three options: (1) take a taxi because it will be easier and quicker, (2) take the Tube because it will be quicker, or (3) new option -- travel to London the night before and spend the morning exploring London, giving ourselves plenty of time to get to King's Cross Station.

Thanks again for everyone's responses. Very much appreciated.

Based on everyone's responses, I have three options: (1) take a taxi
because it will be easier and quicker, (2) take the Tube because it
will be quicker, or (3) new option -- travel to London the night
before and spend the morning exploring London, giving ourselves plenty
of time to get to King's Cross Station.

The taxi certainly isn't quicker because of traffic. Your itinerary depends upon your inbound train from Paddington being on time and everything else being perfect. Your unfamiliarity with the tube adds time which you cannot afford. So option #3 is your best bet and probably more enjoyable/relaxing.

Forget thinking the taxi will be quicker. Traffic is horrible in London.

There are numerous hotels within a block or two of Kings Cross. The British Library is practically next door and a pleasant way to spend some time in the morning.

I have been on trains from Bath that were late. If you miss your train to Edinburgh, you will have to buy new tickets at full price.

I like ChrisF's option. I didn't know you could go Bath-Bristol-Edinburgh without having to go through London.

London is awesome as a destination; terrible if you're using it merely as a connection point.

Marco, we bought our ticket from London to Edinburgh in advance to get the great deal. Now I'm looking at getting from Bath to London, so will be two separate tickets.

OK, so if you are making a through journey, book at ticket to London Underground U12 (not just Paddington or London Terminals) and make sure you are on an itinerary that complies with the minimum connection time. Do this by plugging in the full journey (Bath to Edinburgh) into the journey planner, matching up to your already booked leg for the last part.

By doing this if you are delayed enroute you will be entitled to be accommodated on the next service to Edinburgh and already have a ticket valid on the Underground.

I like ChrisF's option. I didn't know you could go Bath-Bristol-Edinburgh without having to go through London.
London is awesome as a destination; terrible if you're using it merely as a connection point.

No good for the OP though who has already booked a leg (unless it is sacrificed).

The train via Bristol often works out more expensive. Another option from scratch is to fly from Bristol Airport.

In order to arrive at Paddington at 10:39 you are on the 9:13 from Bath Spa. That is the second off-peak train. The first is half an hour earlier and gets in at 10:14. That would make you much more relaxed, save a London night, and if your Bath - Paddington ticket is an Off-Peak Single it would be valid on this train too. Can you get to Bath Spa Station by 9:13?

Even if you have an Advance, losing it and having to pay £48.60 for a new Off-Peak ticket would be cheaper. It all depends on how lucky you are and how risk-averse you are.

I haven't looked up Great Western Railway's Advance terms and conditions, but if they are like the company I work for there is a provision that a booking office can change an Advance ticket prior to travel (can't do this on the train) for a £10 fee plus the difference in the tickets.

But if your Advance was only £17.50 you won't get much back and it might just be worth buying a new ticket for the earlier train.

Do note that for your date there is a yellow triangle on the trains on that line. That is because of the schedule change on May 19th. Probably no or an insignificant change, but we won't know for a little while, about 6 weeks out.

All the more reason not to risk such a tight window.

I haven't looked up Great Western Railway's Advance terms and conditions, but if they are like the company I work for there is a provision that a booking office can change an Advance ticket prior to travel (can't do this on the train) for a £10 fee plus the difference in the tickets.

That is the case with GWR. Although I'm not absolutely sure from what has been said so far that tickets have been bought yet for the Bath-London leg.

I agree with Nigel that your best bet would be to get the earlier train to London - this would mean you were much less stressed.

I would, personally, go for the connection you initially suggested - ~40 minutes from Paddington to KGX - but then I am British, familiar with the underground, wouldn't have much luggage, and have a contactless card I use for paying. If you have to stop to buy tickets and aren't sure about where you are going, it might be pretty tight, especially if there is any delay to your Bath - London leg. Given the cost of buying new on the spot tickets to Edinburgh, I would definitely err on the side of caution on this one!

A great big thanks to everyone who has responded. Figuring out the fares on the trains in England can be very confusing!

We have decided to go from Bath to London the night before our trip from London to Edinburgh (yes, tickets for the latter part of the journey had already been purchased at a great Advance fare thanks to past posts on this forum). Yes, it does cost £10 to change the Bath to London tickets that we had previously purchased.

Just one more question -- people have mentioned that the train schedules may change on May 19. In your experience, what does this mean? A difference of ten minutes, or a route being cancelled, or what? I'm trying to understand how I can pay for a ticket on a specific day and time, but it is "subject to change".

Thanks again, everyone.

Twice a year in the UK - and in most of Europe too - the railways make their long term changes for the next about 6 months. In the UK that is May and December.

Internal diagrams for traincrew and other staff will change around but for the traveling public there is usually very little change.

Sometimes new trains are introduced, sometimes new stations are opened, sometimes there has been improvement work on the track during the year, etc., and this is when the reality of the schedule catches up.

So a few trains around the country will move some stops by a few minutes, most will be completely unchanged to lay eyes. We in the industry get to see the frantically paddling feet under the water, you just see a duck gliding along - or a train arriving a minute earlier than it had done.

It is very rare to drop a route, much more common to add one.

Don't worry, but do check for what may have changed for the trains you intend to travel on.

the train schedules may change on May 19. In your experience, what does this mean? A difference of ten minutes, or a route being cancelled, or what?

A difference of 10 minutes - possibly.
A train re-routed on that day only because of maintenance route and therefore taking a longer time - possibly.
a route being cancelled - Never. Trains are major arteries, Bath to London is multiple trains per hour each with hundreds of people on them. Such things are only ever changed with many months or years notice. GWR (the railway company) has a contract requiring it to run the trains.