Bequia really only has a few "hotel" type options. Old school hotels, Frangipani and Gingerbread. No pools. Beaches are elsewhere. But close to the centre of activity and lots of restaurants to choose from. We stayed in the Fragipani our first two trips finding out where we wanted to stay.
Bequia Beach Hotel is more like a resort hotel. Beach right in front. OK but not great snorkelling.
After that you need to look at houses if you want a pool. But then you need to know what area you want. There are no really bad areas, but there are definitely some preferences.
Lower Bay, great beach, a few restaurants, lots of villas. You will spend time here no matter where you stay.
Princess Margaret, great beach, stupid steep road, one restaurant, a few villas. Always worth a visit.
There are a number of villas on the ridges between these beaches and they are usually a decent choice. An example is Trpoical Hideaway. but there are many other
Then there is the whole remaining 90% of the island.
Wlak and cab, no need to drive.