We visited St. Barts last year by plane.
If I remember correctly it cost roughly 70 Euro each way on a commuter plane from the L'Esperance Airport, St. Martin.
We did not rent a car in St. Martin, don't know if I would bother. But it depends on what you are planning to do there.
We ate a late lunch at a great restaurant for ambience and people watching. http://www.tombeach.com/la-plage-restaurant/
It is a 7 minute walk from the airport. It is pricy but quite the experience. I believe lunch for the four in our party was approximately 400 Euro which included 2 bottles of wine and the lunch lasted 3 hours. We were not rushed out but lingered while we were waiting our return flight. Quite the experience!
To give you an idea of our day there, we took an early flight from St. Martin. We walked into Gustavia, spent most of the day there, ate a light breakfast, window shopped, walked and explored. We then took a cab to La Plage for our late lunch. Then walked back to the airport for our flight back.
It was a spectacular day - well worth every euro!! Would I do it again - YES in a heartbeat!!