I've known this girl for a little while now, and I'm really interested. I don't want to ask her if she's my girlfriend, because I don't want her to feel. If you find yourself in one of those are-we-or-aren't-we phases, and you or so of blissful dating, drop to his knees and declare his undying devotion. start saying "I love you" and being referred to as "my girlfriend" in public.
My teacher crush excluded, as his girlfriend didn't naturally come up while he was teaching us Data Sufficiency. However, it could be very possible the person you are crushing on is in a fledgling situationship, just shy about mentioning their relationship, or is completely single. Internet-Stalk Them CHIX Productions on YouTube Yes, you're right, this isn't so much asking a person if they are single as it is asking Google if a person is single, but I think doing your best internet stalk is the most innocuous and easy way of finding out if someone's in a relationship or not.
You will be able to find out if your crush is in a relationship or not — just be careful you don't confuse a sister for a girlfriend. I'm not suggesting that you necessarily ask them "What are you up to this Wednesday?