I know what you mean. Im like this when im out with my bf (which luckily, i dont do often). When i'm with my mates though, it kind of comes naturally to go have a boogie. I do get a little shy to start off with, as when we start dancing there's not many other people dancing, so i dance a bit wooden, but once it gets a bit more crowded and we get going a bit, i dance like no ones watching, because by that point, no one is, everyones drunk, and everyone else is dancing anyway.
Just blank your mind and wiggle. If your mates laugh at you, laugh back. If anyone else laughs at you, just ignore them, you're never gonna see them again anyway, and if they dance, you can laugh at them. Problem solved.