The timing is a little tricky...I would buy the bus pass definately. If you get in at 3, I'd hop on the ferry to Hamilton and explore.
I'd take the bus to horseshoe beach the next day. Remember to bring a change of clothes. They frown on you riding the bus in a wet suit. They have changing rooms with showers. Then I would hop back on the bus and ride all the way to St George and ride the Ferry back to King's wharf. You'll see the whole island and then get a different view of it frm the ferry...and don't worry, it's included in your bus pass price.
I'm a worry wart, so I would spend day 3 exploring King's wharf. There's a cute little beach called snorkel park right there. It's got odd hours, I think it doesn't open til 10, then they close at 5 and sometimes hey have a beach party at night.
Whateve you do, bring rain gear, because it's not unusual for showers to crop up.
Have a great time, it's a beautiful island.