Hate to be the bringer of bad news... but when I shaved my bikini area I always had problems because the hairs are courser. I always got ingrown hairs, and razor rash. (those little red bumps!
So not being able to help you with that problem, I'd recommend laser. I have gotten my bikini done over the past year, and it's truly wonderful. Money is a bit of an issue, I'm in Canada and it cost me $100/treatment. You can end up needing 6 treatments, usually 4 weeks apart, towards the end it becomes more like 2 months apart. It is a permanent hair removal treatment.
The only cautions with this is:
-Make sure the place you go to has a "permanent" treatment, some lasers simply get rid of the hair only for awhile.
-Use topical anaesthetic such as "Emla" cream to numb and help with pain for the area being treated, trust me, you'll get a better effect if you can use a more intense laser to zap the hair
-Don't expect perfect results. The laser gets rid of 80-95% of the hair, but some hair (which is thinner thankfully) can come back, and right now I'm getting electroylsis to touch up these ones. (which I might add is very cheap, and you don't need Emla cream during the procedure)
Anyways, I'm really impressed because I hated the rash I got and my bikini area never looked good. Now I've been swimming a bunch of times not embarrassed of my bikini area, it looks perfect!
It's nice because I am starting on my armpits, and soon the only thing I'll have to shave is my legs (and that doesn't bother my skin like the other two areas!)
Good luck to you, I hope this advice helps, or think about it for the future.