When we were in Nassau we spent a couple hours sightseeing the historical landmarks, a couple hours at Cable Beach, and then a couple more shopping before going back to our ship. Being our first time to Nassau we wanted to try to fit it all in. Knowing what we know now, and seeing what we did, I'd recommend skipping the historical stuff as well as the shopping. I'd spend a few hours at Cable Beach and then go back to the ship.
The bus system isn't a hassle at all. It's not a big bus crammed with people. Ours was more like a large minivan that had just a couple other people on it. You walk on, hand your dollar to the driver and take a seat. No muss, no fuss. Easy as pie. And tell the driver when you see the hotel where you want to stop to walk through to the beach. He'll just pull over right there in the middle of the road and let you out. Again, no problem.