Some of the cheapest places on on the island are Tina's Hostel, Tom's Hotel and Mira Mar Hotel. Being here in May will give you access to cheaper prices since we do not have a lot of visitors around at that time. You might want to bring a friend but Caye Caulker tends to be quite safe for a single female as compared to other parts of the world. Everybody pretty much everybody else here.
For diving you can trying Frenchies, Belize Diving Service and Forever Young Divers.