The Roman Baths are in Bath, not Bristol, so you'll want to plan on travel time. You can get the x39 from Bristol to Bath, which is about a 45 minute trip, the train from Temple Meads is about 15 minutes, or you can attempt to navigate Bath with your car. I recommend one of the first two options! The baths take as long as you make it. They have an audio tour, so it depends on how many 'stations' you listen to and how much you read. It definitely won't take the whole day and there's plenty of other stuff to do in Bath. There's a free walking tour that starts in front of the baths at, I believe, 10am. If not, it's 2pm. It's a great destination for a day trip. I recommend the Riverside Cafe which is just below the Pultney Bridge for lunch.
I've never geocached in Bath (or anywhere else!) so I can't really comment on that!