It's not necessarily always the same. It's not like all agencies follow strict procedures with each girl. If you're going on an open call, they might not ask you at all (this has never been my experience) but if you have a meeting set up already it seems more likely.
It's a good idea however to have your bikini underneath your clothes (or bring it along with) in case they do want to see you/Polaroid you in your swimsuit. When I met with MC2 I didn't have my bikini with me and they asked if I'd be comfortable being photographed in my underwear. You'll probably be asked, but who knows. Either way it's best to be prepared, right?
And I think as long as you look your best, the hair shouldn't be an issue. Whatever makes you look good is the way to go. They might want to know what your hair looks like naturally, but I don't think it should be a big deal if it looks good, you know?