I am not sure if they offer a shuttle, but it is a 45+ minute drive to something the you will want to only spend an hour or so at. I just came back from St. Lucia on a research for wedding mission, and the Fish Fry was, nice/OK, but not anything to rave about.

Possibly from those place you can arrange a water taxi ride which will make it more of an adventure, and take a little less time.

If you are considering both of those resorts here is a little summary of each from my view.

Jalousie- very high end resort, and has the only white sand beach on this end of the island, but you need to take shuttles to and from the beach and your room because of the size of the plantation. Though it is very beautiful. If you are the type to want to just go and stay on the resort this is a good place. This is situated between the Pitons so it has a very dramatic view from everywhere.

Stonefield - beautiful more cozy place with a small restaurant and villas with great views. You will need to take a shuttle to the beach at Jalousie which Stonefield offers complimentary