A Brazilian bikini wax removes hair from the entire pubic region and the area by your buttocks. The waxer leaves a small, optional patch of hair above the vaginal area.
A bikini wax, I think, just removes the hair just outside your vaginal region. I read that you can ask for a full bikini wax, which would remove most of the hair on your vaginal region. That sounds like a good option for you. Once you find a salon you like, .I would call them up and ask what they offer and how they can accommodate you.