Of course it's possible. This is assuming you're a guy. If you're a girl it might not be as easy, since there might be different dynamics involved.
I've had a lot of friends over the years that I've managed to get into relationships with (I'm a girl), and afterwards I've remained friends with all of those guys. I don't have any particular knack or talent for this, it just seems to be the way it always ended up working out. So you shouldn't worry about spoiling the friendship if a relationship doesn't work.
As for getting to the relationship part, I'm afraid you will just have to find the balls and make the move. You say you see a lot of her, but if you haven't already then getting her number is a good first move. From there, I usually work up to the point where we spend a decent amount of free time together, just the two, and become really good friends. That makes the transition really quite easy, and asking them out wont seem so out of the blue.
Go for it. If you don't ask, you don't get.
But a word of warning: if the relationship messes up in a really bad way, it will have the potential to make things awkward. But if you're both adults about it, you should be OK.