London to Bath (or Windsor or the Cotswolds) via rail

1) I try to avoid Friday and Sunday rail travel as it can get very busy.

2) GWR is the train company that operates trains from London to Bath.

3) A rail card might save you money but if you are only going on the one train trip to Bath it may not be worth it. Others will have more information.(The tube in London isn't included.)

4)You could take a coach. National Express operates from the Victoria Coach Station which is even closer to you than Paddington. The trip is longer but cheaper. The Bath Bus Station is next to the Bath Train Station.

5) Instead of Trainline, which is a third party reseller, use the official UK train website: http://www.nationalrail.co.uk.
There you can get the schedules, prices and it will take you to the actual train operator to buy the ticket. $158 can be too much depending on the day, time and type of ticket you get. There are two basic tickets: Advance and All Day. Advance tickets are cheaper and only good on a specific train. All Day are good, well, all day. It can get a little more complicated than that but I'll let others get into that.

Windsor is an easy trip from London and no advance tickets necessary. It's basically a commuter line.

The Cotswolds are also available but hard to get around without a vehicle. London Walks sometimes offers day trips out of London to the Cotswolds. If not, there are other companies. Mad Max offers day trips out of Bath.

Looking on a sample day- June 6- a Day Return to Bath will cost you about £62 each return ($74US) on Advance (Specific timed tickets) or £100 return ($120) on a flexible ticket after 0930, £73 return ($87) after 10.30am.
A Two Together Railcard costs £30, and gives you 1/3 off so pays for itself after a total of a bit under £90 of rail travel, which you will reach. Valid after 0930 on weekdays, any time weekends- the above train time restrictions also do not apply at a weekend.

On the same date Moreton in Marsh (for the Cotswolds) is about £40 each ($48) on Timed Advance Tickets or £69 each ($85) on flexible tickets. There are clever and complex ways to bring these costs down but those are the straightforward fares.

Others can give you the advanced tutorial on how to make the tickets very complicated and not save very much by doing so.

If you buy a paper ticket from Paddington to Windsor (rather than paying contactless) you also benefit from the Two Together discount you pay £14.20 ($17) each after 0930 outward travel or £9.35 ($12) with your railcard. Just buy that at the station on the day- same fare if you buy it today or 2 minutes before travel.

So in brief the Two Together Railcard is worth getting for you, and an aggregate total of around $158 each for the three trips is a bit high, but not totally unreasonable.

There is no sensible bus from London to the Cotswolds,

On the coach the return fare to Bath is £15 to £20 ($18 to $24) but the first direct bus is at 0900, arrive 1200- rather late.

Yes there is a bus from outside London Victoria to Windsor at least hourly, cost £2 each way- but it takes 1:45 each way.

So essentially it's up to you to trade off price and convenience to Windsor and Bath.

The Man In Seat 61 has done a video of London to Bath by train.

Just another thought- for these trips it may be worth getting a Britrail London Plus Pass- 3 Days in 1 Month. As far as I can see that currently costs £116 ($140) but the point is that it gives you total flexibility of which trains you use- so no trying to get cheapest fares and being stuck with certain timings. Also no need to buy a UK railcard.
If you are over 60 it seems to be £99 ($120) each.

We can't buy them in the UK so I have to assume the prices I am seeing on https://www.internationalrail.com/453f-Other/a6ca-britrail-london-plus-pass are correct.

Perhaps someone in the US can confirm.

q1 - no. Thursday is the new Friday, Tuesday is the new Monday. Check if work is being done on the line and Saturday has football, but not in summer.

q2 - the same as the difference between airlines. Some use one equipment and others use different, but they all get you from point A to B. Different ones connect different airports or stations. GWR paints their trains green or blue.

q3 - you only know if you need a railcard (actually nobody actually needs one, but they can save money) if you work out how much you will spend. You save 1/3 on many tickets but you have to pay £30 for the card. Some you have to qualify for, usually by age, but the Two Together and the Family and Friends are for any age. Two together means both named are travelling at the same time all the time. Family and Friends requires at least one child and one or more adults.

q4 - you can, some do, including the prior answerer, but I never do.

q5 - look at national rail and look at the options (in the currency of the country, Pounds) and restrictions. Look at different times of day, different providers, and compare buying now, tomorrow, three weeks out, you will see differences. Basically, the higher the demand, the higher the price until you are paying the walk up price.

There are walk up prices, available up until just before the train leaves which are the highest. You can have First Class or Standard. First Class usually costs significantly more, and what you get for that extra money varies from nothing more than a door, to food and drinks and a very comfy seat. Walk up prices are often divided by Peak and Off-Peak, based on travelling before the end of rush hour (usually 9:30am) or during evening rush hour (4:30pm or earlier to 7pm or 7:30pm). Peak is usually much more expensive than Off-Peak.

You can also often get what are called Advance tickets. Those fares can be a real bargain. But they are not available on all routes or at all times of day, and they tie you to a particular train time on a particular route, effectively non-changeable and non-cancelable. You can but it is expensive and you have hoops to jump through. Sort of like missing a plane.

So it will benefit you to read The Man in Seat 61 and learn from his expertise. I've just scratched the surface.

As to specifics of GWR as opposed to some others it is now rather more of a leisure-orientated business than it used to be having its close to London commuter services taken over by the Elizabeth line, & the demand for outer commuting somewhat reduced by changed working patterns.

Its leisure traffic particularly at or around weekends exceeds that of pre covid times. Hence really cheap Advance tickets are harder to get but ones a bit cheaper than flexible fares tend to remain available close to day of travel (generally undercutting split tickets a bit).

thanks to all who have responded....I really appreciate the insight!!