It's really not as bad as you think, and it is way better than razor burn.
BUT, you need to make sure that the place you go to has a good reputation, and which does a lot of bikini waxes on a regular basis, because there is obviously potential for things to go wrong. So find a good spa, and spend a little more. Your body and dignity will thank you. Aveda certified spas are generally very good, and you'd probably be surprised they're not really more expensive than lesser spas.
If you're just getting a standard bikini, most places will have you keep your underwear on. If you're getting Brazilian it's all coming off. But even then, provided you followed advice above and get an experienced pro, there's no reason for embarrassment. They do this every day and probably see more cooch than your family doctor. You won't phase them, and they won't remember you. Obviously you want to be as clean as possible for everyone's sake.
So, two rules to follow.
1) Go to the best spa (with experienced waxers) you can afford
Well, I have never done it but I know a friend who did and from what she told me. It wasn't that expensive. I think it was under 100 dollars. Around 50. But then again it depends on where you go to get it done. I'd suggest go to a local salons, you don't have to go somewhere expensive. Oh and hurts too. Obviously. Just like it would if you waxed your arms. But since "down there" is more sensitive, the pain would be above average. The pain also depends on the amount of hair you have and how thick it is. But. The hair doesn't grow back as fast. So that's a plus.
I've never done it and I'm thinking of doing too just for myself and see how it feels but all my friends who've done it - all said the same thing "it hurts like a b@%th" (yea I really don't know if I can say it here never really came across it up until now)
Actually, in response to wildd's answer. I actually would recommend you NOT go to a local place. Getting waxed down there will probably be very embarrassing and do you want to run into the person who saw your goodies at the supermarket? I mean, I know they are professionals, don't care and are used to it but you aren't so you'll def. Be uncomfortable. I'd go somewhere a little away from home.