Advance vs. Day of - Rail tickets

Trains in the UK never sell out, They may be standing room only but they do not sell out. But unless there is service disruption or an event on standing to Bath or Oxford is pretty unlikely. The trains generally run with enough capacity.

Advance tickets are cheaper but in the modern (Post Covid) age Advance Tickets are available until midnight on the day before travel (on some routes until 5 minutes before). Yes, at a higher price than weeks before, but still at a good discount.

So you could make a decision a day or two beforehand.

Many people here are madly scrabbling round getting tickets months- I get the same fares as they do booking two weeks to often 7 days before, then the fares gradually rise.

Both Oxford especially and Bath are routes you can always get short notice Advance Fares on. For Oxford remember there are two routes to look at- out of Paddington on GWR and out of Marylebone on Chiltern. Sometimes one or the other has the better fares- no hard and fast rule,

No, the train won’t be sold out. Note that departures from London Paddington before 9.30am on weekdays tend to have higher prices but on weekends that is not the case. However, I would avoid Sundays as that is when engineering work is more likely and services will be taking place in Bath Abbey.

You may find it works out cheaper to buy a return ticket PAD > Swindon and Swindon to Bath even though you stay on the same train.
You can also buy advance tickets for specific trains once you know when you will be going.

Advances on GWR evaporate more quickly than on some other operators, especially to/from London. For example for London to Bath there are none available today or tomorrow and on Tuesday they are only a few pounds under the super off peak price. Go ahead two more weeks to skip over Easter and they are a little cheaper but still way over the theoretically available cheapest. There are other tricks to reduce costs such as split ticketing if the train stops at the intermediate point.

London to Oxford is a bit different as cheaper advances are often available at short term on the Chiltern route which has been downgraded to slow services only by and large - half an hour longer typically than from Paddington.

Also 6 May is a bank (public) holiday but I guess you won't be doing a day trip right at the start.

Great input! Thanks to each of you for your replies.