I want to say that the NS fuel docks all open at 7am. Did a quick search online, but was unable to confirm that.

Depending on your goals, Marina Cay can make for a decent stop off point on the long sail from Anegada to JVD. That would probably be my recommendation, unless you were trying to get well offshore to fish the banks or something like that.

EDIT: Hmm, just found the hours on Leverick's website and they open at 8am. I would guess Bitter End and Saba are the same.