Island hotels are poorly presented in international booking systems.
Anyway you can find good options right on the beach. If you are traveling with a tent, you may stay at Ivan's Campground
, located in the eastern part of White Bay
beach. Find hotels in Jost Van Dyke
How to get there 
Fly to St. Thomas Airport (STT)
. (Most likely, that cheaper option will be to fly first to San Juan Airport (SJU)
, and next fly to St. Thomas). In St. Thomas airport find shuttle bus going to Red Hook
ferry pier. Next take a boat to Jost Van Dyke
island (via St. John island and Tortola island).
Note, that British Virgin Islands has its own airport - Beef Island / Tortola Airport (EIS)
, but it serves very few flights. Find flights to Jost Van Dyke
When to go 
Any time of year. Winter weather is more comfortable, but too many tourists are everywhere. Warmer water is in the summer and there's no crowds, but sometimes hurricanes happens (not every year).
Water temperature, C
Wind speed, meter/sec