You won't die if you approach them. Just say something that suits the situations: ask where this class is or where library. It only gets easier after that. You won't care after nth approach. Remember only you determine your self-worth and if you get rejected, she's rejected your approach, not you as a person.
Wondering what if for DAYS is much worst than the very brief ego kick you'll get from rejection. Kill your ego, that is the key to eliminating approach anxiety, deltabeta gives you one way and that is to separate yourself from your actions... this has the added benefit of being able to look outside in and see what approach methods are working and what don't. Think of it as an experiment, take notes just start getting to work.
I promise you that approaching'll never be easier than it is in college--especially if you live on campus. But even if you don't you're not really 'strangers.' Basically my strategy my first semester at the two different schools I went to was to introduce myself to as many people as possible and then to introduce those people to other people.
If you're college is huge on Greek life, the bar scene, etc. it'll be tougher--but even then there are tons of people there who wish they had a bigger social circle but are too insecure to expand beyond whatever small clique they settled into.