How can I approach this girl, and should I even bother?

No. Do not bother

How rich she is shouldn't matter, because whether or not you guys connect is ultimately going to be much more important. If you guys both share a couple of common interests, that's great, use one of those things for an opening line. Just make sure it sounds smooth and you're not acting like you just want to get with her. Then if she seems interested in you keep talking to her after that. If anything you'll have an advantage over the other "cooler" guys because you have something in common with her when they probably don't. And I've seen a lot of hot girls hook up with guys who aren't "cool" so don't even worry about it.

When I first saw Cassie, she was sitting on a bench reading a book. I had no idea if she was even into girls. She was just so beautiful, that I could not let myself miss the opportunity. I couldn't help but think that even if she was into girls, she was waaaaay out of my league. I worked up the courage withing myself and went over to talk to her. We've been together for more than 3 years now!

Truth is, this girl you like is just as human as any other girl you know. I say go for it. You really have nothing to lose.

Basically, if you don't think she's worth the risk, then you really don't like her all that much.

Go for it, and good luck!

just try and start it off bring up a past encounter.

didnt i meet you once at [place] a while ago?

hey you were in my art class last year.

or whatever.

just ask her how shes been, start a simple conversation. you mentioned music, talk about a new music album u just got or something and act REALLY excited about it. Tell her to check it out and have her tell you what she thinks(myspace just launched that new amazon.com partnership so she can listen for free). Ask her for her number and see if she just wants to text once and a while or something. And of course, mention you were glad to run into her.

yeah she will be taken back at first about the random conversation. but it sounds like you just need some way to communicate more than "a couple of times".

But what else are you going to do to get her number? take it out a friends phone? haha

If you feel those couple of times you spoke that there was a connection and she generally seemed interested in you, you have to pick up on the vibes she sends when she talks/smiles at you...if it's inviting then you would obviously have a chance.

have a crack at it, the worst that will happen is tell you she's not interested. at least you'll know. maybe she likes you too? or even if you can't be "together together", you might still be able to be friends because you do have those few things in common (even if that's not exactly what you are looking for)

at lunch, go up. sit down. feel your face get red, and say... this is critical... "Hey." ignore all the stares you think you are getting and enjoy your food. maybe say, I heard you like art and music....

Her family is wealthy.........so what? You want to be with her ......not with them......so be a friend to her and let her know that you like her......