I've done this tour twice now, and I think I've finally figured out how to get the best out of the 24-hour ticket. Go to the Tower of London as early in the morning as you can (see my other review). When you've finished there, go buy your bus tickets or get your e-tickets validated from the rep at the bus stop near the tower. Then go back to the tower pier and take the free boat ride that is included with your tour. This way, you'll see all the same bits as the bus tour when it goes along the embankment, but from the water, which is really the way this part of London should be seen!
You'll be let off at Westminster, where you can then board the bus tour. Make sure to get on the red route, as this is the one with the live commentary in English, and it takes you to all the major sights. You'll probably have to switch buses or get a new driver at Green Park, as this is where the tour officially "begins," but use the 15 minutes or so to use the toilets in the station and get yourself a snack. Then stay on and see all you can see until they kick you off for the day (usually 5 or 6pm).
As you have a 24-hour ticket, the next morning, you can get on the blue route and see what the red route misses. It's not much, but if you're not sick to death of the bus, you may want to do it. I realize I haven't said much about the tour itself, but it's pretty standard, usually with funny commentary, loads of history, and a great way to see and learn a lot in a short period of time.