London to Bath

Bus from Heathow to Bath takes about 2hrs 20 mins https://www.nationalexpress.com/en

But if you feel that ‘s too long then take the RailAIr coach from Heathrow to Reading.
https://www.firstgroup.com/berkshire-thames-valley/rail-air

Then train from Reading to Bath (from about £13) http://www.nationalrail.co.uk/

For train tickets the cheapest are called Advance (on sale about 12 weeks before date of travel).

For Bath to Southampton and Southampton to London train is the best. Once again look for the cheap Advance tickets on the nationalrail site.

Are you arriving from the USA, so possibly jet lagged? Have you done this before and are therefore happy with such a long day at the mercy of public transport?

You are likely to be out of the airport somewhere between 7.30 and 8.30am. Unless you get the slower bus, there is no direct rail connection to Bath, so it’s either into central London and out again or do as the previous poster suggested and take a bus to Reading then get the train. This probably won’t work out much quicker than taking the bus by the time you have worked out where to go at Heathrow and in Reading. You will presumably want to store your luggage somewhere in Bath before you start looking round.

Bath to Southampton by train is c 1.5 hours.

Rail fares are generally cheaper if you book a non-flexible ticket, travel after 10am weekdays and 11 weeks in advance. The difficulty with a non-flexible ticket is that if your flight is delayed, then you would miss your train and have to buy another walk-up fare, which will be expensive.

You aren’t going to have much time in Bath and may want to consider something less taxing if you are going to be suffering from jet lag.

Both train and Bus from London Heathrow to Bath is about the same travel distance in hours. The only difference is the price since the train will cost more. You can take the National Express coach for less and arrive in same amount of time to Bath. Since you will be landing at Heathrow on Apr. 26th at 6:30am, if you can clear customs quickly, you can take the next National Express bus service to Bath leaving at 7:55am from Heathrow and it will arrive to Bath at 10:15am, but if you were unable to get through the airport lines, then the next bus service would be at 10:20am and will arrive in bath at 12:35pm.

Pick Up and Drop Off

Terminals 1, 2 and 3

Pick up and drop off points for Terminal 1, 2 and 3 are located at the Central Bus Station, which is just a short walk from the check in area and is clearly sign posted from around the airport.

Terminal 4

National Express coaches will pick up and drop you off at stops 13 and 14 just outside the Terminal 4 building, and transfers to Terminal 5 and the Central Bus Station can be made via stop 7.

Terminal 5

National Express Coaches to Terminal 5 will use stops 13-16 just outside the terminal building for pick up and drop off. Other National Express coaches can be caught from stops here, including destinations such as Oxford, Brighton and Reading.

we are trying to squeeze as much as possible into the short time we have.

IMHO then you should spend the day visiting London instead of riding buses and waiting for buses. I took this bus and it was a smooth trip so no issues there. But planes can be delayed so you might not make that first bus out so you'll be cooling your heels in the bus station waiting. I should add that the route to the bus station at Heathrow isn't well marked; we followed a series of signs that said "buses" and ended up at a local bus stop in the parking garage, not the right place.

I agree with John, you'd be asking for trouble by trying to go to Bath on that first day. Get settled, see some of London's myriad sights, and start out a little more refreshed for your Southampton adventure.

If a visit to Bath is a top priority for your trip, why not use one of your days at the end of the trip to go there? You could go directly from Southampton to Bath

(see https://www.rome2rio.com/map/Southampton/Bath )

and then take the train from Bath to London to see some more of London's sights on your last day.

I have taken the direct bus from Heathrow to Bath and it works fine. My wife and I had pre-purchased and when our flight arrived late we missed our bus. They gave us a ticket on the next bus for a nominal charge, less than $10 per ticket.

However, I don't think your plan is advisable as your only day in Bath will be a jet lagged one. (Unless you are coming from elsewhere in Europe).

Thanks for all the replies and advice. You all have some very valid points. Especially about the jet lag.

Yes, we will be coming from the USA, Northeast Texas, to be more specific. 6 hour time difference.

Considering some of the opinions given, I may reconsider and head straight to Southampton and take it easy, around there, and be able to sleep in a little before heading to the ship the next morning.

Thanks again for everyone's help. This will be our biggest adventure, so far. We went on a New England/Canadian cruise, last year, and thoroughly enjoyed it. We are very excited to finally get to see a little of Europe.

I think if you decide to go straight to Southampton the first day, you won't regret it. It will give you a chance to adjust before you board your cruise ship. If you have the energy and inclination, here are some things to see & do in Southampton. http://www.world-guides.com/europe/england/hampshire/southampton/

Bath is wonderful, but I strongly advise you to change your plans. Yes, you can take the train, but if you rent a car, traffic can be terrible in the South of England.

I suggest considering Winchester instead. It is fairly close to Southhampton/

I should add that the route to the bus station at Heathrow isn't well
marked; we followed a series of signs that said "buses" and ended up
at a local bus stop in the parking garage, not the right place.

I wonder if this is because in the UK they differentiate between buses (short trips, within a city) and coaches (long trips, between cities). I don't know; I'm just speculating that the signs might have reflected that. I'm sure one of our British friends can help.

Thanks guys,

We are now considering Winchester and Southampton. I am also learning from the suggestions and advice about the different forms of public transportation.

A late post here from a fellow Texan who loves the UK. If you’re going to Southampton and have the day ... consider a taxi/bus to nearby Portsmouth. You can tour the HMS Victory and see the spot where Nelson took the fatal bullet at Trafalgar. It is an awesome tour!

Have you considered a private car service to Southampton? You will be tired, sleepy, jet lagged, and on unfamiliar ground. That's when having a private driver meet you in the terminal and whisk you to your hotel is a godsend. Yes, they can be expensive, but for two people it might not be that much more. It is one of the few indulgences we don't mind spending a little more to enjoy. We've found that car services in the destination city usually work out best as they always seem to know the best way "home".

Of course trains are cheaper if you buy ahead, but then there are the logistics of allowing enough time after your arrival to be sure you can catch that train. And then having to make connections, schlep the luggage, and etc. Just something to consider.