Is it aginst the law to land a small plane on a Rural grassy runway on a island?

Yes, you can land it there if you follow Bahamas laws. You must report to a customs office within a certin amount of time after landing. You can even land at a major airport in Bahamas, get a visa, go through customs, and then proceed to grass field. In my opinion, u could prob land on the strip and go about your business, and probably will not have any issues, but if u get caught, look out. I had some friends who rode jet skis from Miami to Bimini, Bahamas. It was a 58 mile ride. Upon arrival, they proceeded to the customs house, paid a 150 dollar boat permit fee, where issued "yellow flags" to place on their skis to show that they had paid their permit fee and had their passports stamped. I've attached a link to their journey below. There is a part 2 link also, once you open it up on u tube.