The letter is a bad idea. She will think that you're deranged. It's one thing for you to be attracted to a stranger based on her appearance. But it's crazy to have strong feelings for someone that you've never even talked to.
Have you ever heard of small talk? You can start talking to a total stranger about non-threatening, minor stuff, like the weather. Walk up to her at the bus stop and say something about the weather. Better yet, ask her a question about the weather, as that will require an answer, even if the answer is "I don't no." Start with the small talk and try to build upon that. Some other safe topics are new movies coming out, celebrity gossip, local news, her shoes, stuff like that.
Good decisions come from experience. Experience comes from bad decisions.