We were staying in an apartment near the Royal Crescent while we were in Bath, so a bus stopped almost right outside our door. (If you were on the field in front facing the Royal Crescent, the bus stops on the corner of the street you'll see to your right.) We simply hopped on and paid the driver for our tickets. These included a transfer to another bus that explored gardens outside the town center, as well as 15 stops in town where we could hop on or off at will. An extra bonus was that the tickets worked for 2 days. Tour aside, this was a great convenience when we didn't want to walk from one end of town to the other.
So what was the ride like? The double-decker buses are very comfortable, and the boys made a beeline to the top section. We were all given headphones we could plug into our seats for running commentary about the town. While the recorded commentary was certainly useful, I enjoyed a tour with a live guide onboard the most. Your ticket covers the cost of either; it's just a matter of waiting to get on a bus with a real person talking. Some of the highlights included High Street, Grand Parade, and Queen Square, where the Jane Austin Center is located. The guide who we eventually had the pleasure of hearing was very pleasant, with plenty of interesting tidbits to offer. For instance, she told us that men started opening doors for women because dress styles such as the hoop skirt that was popular when Bath was at its height of popularity made it difficult for women to reach forward far enough to grab a doorknob. Therefore, a lady's escort had to open the door for her!
I would highly suggest this type of open-air tour if you have kids in tow. Even if they don't pay attention to all the details, they'll enjoy the ride.