I highly suggest you do NOT rent a car. There is more to Jamaican driving then just driving on the left hand side of the road. Their rules and culture of driving is completely different from the US. You would be taking your life into your own hands by doing so. The roads are not marked real well and you must know where you are going. It really isn't a good idea to drive yourself. You would just be asking for trouble.
Just so you know, the bus ride isn't like a great big grey hound bus. It is a mini-van that can seat up to 5 couples. If you still don't want to do the shuttle ride, then you can hire a cab to take just you and your wife to the resort. It won't save you anytime to hire a cab.
While you are at the resort, the tour desk will be happy to set up a driver for you to take you around the country.
I'll state it one more time for emphasis, DO NOT DRIVE YOURSELF!
Juliann & Jeff
Jamaica Soon Come