I'm single and been noticing a few ladies I'd like to get to know better, one that I see twice a week in the science lab center at college, she's in charge of watching the lab later in the evening, she is very focused on her studies and always gives me a friendly smile when I come in and always bids me a good evening when I leave. I know people give common courtesy but I feel its a little different, but my true question is and maybe you girls can help me, is it too impersonal for an icebreaker to give her a letter to asking her to take her out for an nice evening getting to know one another.
I think it would be better to ask her out in person. It is impersonal to do so in a letter. But there's nothing wrong with writing down the things you'd like to say to her so that you'll be less nervous. I'd recommend making a list of a few things you'd like to say to her and go over them a few times so they'll come out a little easier if you're shy/nervous.
She may just be polite in her communications with you thus far. It would be better if you could find things to discuss with her to see if you have anything in common before risking possible rejection. She may have a boyfriend and that's something that you could determine with just a little conversation at the lab. You both have something in common being that you're in the lab together. Start talking about that and get to know her a little better - her interests, etc. If you have something in common with activities outside of school, start there. Maybe you could do one of them together.