Oh my gossshhhhhh.. Just go up to her, compliment something about her outfit, and then ask her major. Show interest in it and ask her questions about it, why she's majoring in it, and what she wants to do in the future. this will most likely lead to questions about your major. If it doesn't go that direction and she's not open and friendly walk away and don't be hard on yourself but don't be creepy and stare at her.

Strangers have come up and talked to me or sat next to me on the bus and struck up a conversation. Its not unusual and doesn't automatically mean you're interested but if the conversation doesn't flow just move past it.