We were there in 2006 with HAL. I don't recall that there being buses available at the taxi stand for an alternative island tour. This is the link to the Grand Turk Cruise Center website - it may have the information you want. http://www.grandturkcc.com/
Took a cab into the town, which at that time was $5 each - not round trip..... Small town with not much to do or see- however the people were very nice. There is a little museum, but the entrance fee was $10 per person - and after spending th $10 to get there, we didn't want to spend that much. It was a lovely little island. Tablemates did the bus/island tour and enjoyed it - especially the stop at the lighthouse. If you snorkle, the water was excellant.