No regular bus or taxis go there. You could find some taxi who would take you out there, then hope he'd also come back to pick you up at some set time. Or--if you're up for the walk, you could take the Maho Shuttle from Cruz Bay and get off on the Leinster Bay road and walk the rest of the way, then plan to try to catch it on the way back. Or, you could hitchike (which is much more common on STJ than on the mainland.

You don't mention why you're not renting a vehicle. That would certainly be the most convenient way to get yourself to Leinster. If it's finances, consider that taxis fares add up. Or--there's several good beaches/snorkeling spots that are much more easily accessible without a vehicle than Leinster.

Thanks for your help Nick. I am renting a car part of the week on St. Thomas, but already have reservations for snuba on St. John on a day I don't have the car. After reading your comments, I am considering getting a vehicle after ferrying over to St. John. Thanks again!

You won't be able to reserve a car for one day but depending on when you go to USVI, you can usually get a 'walk up' for the day. High season is a little tough while low season is no problem.