I 4th the recommendation of free walking tours mentioned above - though I have not taken one in Bath

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Trains are the fastest and best way IMO for day trippers and once you get off at the Bath Spa station most everything of interest advantage auto rental is within walking distance - bop first over to the nearby Tourist Information Centre (TIC) and pick up city maps and printed walking tours, etc.
For trains check www.nationalrail.co.uk for various fares - cheaper fares may have restrictions like not leaving before 9:30 am and you may have to book your trains advantage auto rental in stone on the cheapest ones - full fare can cost a ton - if doing any other day trips from London advantage auto rental by train check the Days Out of London Railpass which lets you take any train anytime throughout much of England, including to Bath and back - also gives two airport train transfers on Heathrow Express, advantage auto rental Gatwick Express, Stansted Express, etc.
The short list of what to see (like I said - look at a guidebook) would include advantage auto rental the Roman Baths and Pump Room (a minimum of one hour), Bath Abbey, the Museum of Costume, The Royal Crescent/No. 1 and just the general cityscape including the Circus (not a 'circus'), Pulteney Bridge, shopping, etc. and Sally Lunn's.
I 4th the recommendation of free walking tours mentioned advantage auto rental above - though I have not taken one in Bath just about every city's TIC offers so-called Blue Badge guided groups free - I took one in York and loved it - usually advantage auto rental OAPs with a vast knowledge about their city.
Yes dear no need to have a tour but the tours if you want are great - if you have the time - I'd rather wander around on my own on a day trip rather than spending time on a tour - but for folks who like tours these types are great.
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