We've done this twice, using the anchorage in the Soufriere Marine Management area for the last stop on St. Lucia, then getting an early start and sailing all the way to Bequia to clear in. The anchorage in the SMM has moorings but, in my opinion, not enough and the boat boys there seemed to be "reserving" them for their clients. We ended up needing to anchor stern to near shore and tying the stern to a tree.
The sail to Bequia is long, but fun and we arrived there in plenty of time to clear in.