Asking a girl out isn't particularly difficult, but it can seem that way. If you want to ask a girl out, but don't want to risk face-to-face rejection, you can shield yourself by writing her a nice letter. A letter can help you express yourself without succumbing to nerves, while showing her how much you like her and want to spend time with her. The key to a sweet letter is that you be honest, true to yourself, and make sure you express yourself clearly.
Jot down a couple things you like about her that are unique to her. This will make your letter personal, which will in turn make it more authentic.
Focus on a couple of the qualities from above. Your letter should be short and sweet, and if you focus your energy on fewer qualities you will come across as more genuine.
Be honest, and tell her exactly how you feel. Don't go over the top with compliments, but clearly say that you like her, and why.
Be yourself in your letter. If she finds you funny, you may be tempted to be really funny; if she thinks you're nice, you may be tempted to be extremely nice. Try and avoid this, as you'll seem insincere, and she be as interested as she could have been.
Ask her on a clear date. Rather than saying "Let's get coffee sometime," say "I'd like to meet you for a cup of coffee at . . . " Suggesting a specific time and place, will make it will be easier for both of you to follow through.