If you are staying in Bath for a whole day or two and would not want to spend a dime paying for a hop on hop off bus or just love to walk around as your are physically fit, then no problem as the City of Bath is relatively small area and most areas are quite flat and easily walkable and the major attractions in and around the city like the Pulteney Bridge, Roman Bath, the Royal Crescent, Bath Abbey and more are fairly easy to walk to (again if you are fit). just be careful of the ancient roman road like areas around the Roman Baths as the square stone surfaces of it are irregular and you might slip if there is some rains as it tends to be quite slippery.
By far the best way to get around the centre of Bath is to walk. It’s a compact city, and with historical buildings on every street and a large number of interesting one-off shops you’ll find something interesting to look at wherever you go. There are plenty of sign to direct you, and most hotels have free maps of the city available, as does the Tourist Information Centre in Abbey Churchyard. Take comfortable shoes though – cobbles, wonky paving stones and the many hills mean that you won’t get too far in stilettos!
If however you have too little time to walk everywhere you want, or if walking is difficult for you, you could take a tour on the “Hop On – Hop Off” sightseeing bus. As in many other cities, these loop past all the main sights and your 24 hour ticket allows you to get off the bus and on again wherever and as many times as you wish. Your bus ticket also entitles you to discounts (usually 10%) at many of the city’s attractions. Prices range from £6.00 for a child to £11.00 for adults, with family tickets available for £25.00.
One of the best things about Bath is that the city's three main attractions, the Roman Baths, the Bath Abbey, and Pulteney Bridge, are all within walking distance of each other. In fact, they are so close together that you could probably get them all in one photograph if the baths weren't below ground. This means all you need to get around is a pair of shoes, though I recommend also taking a bus tour of the city so you can get a narrated history as you ride around.