Ask casually, and I would try something better than a movie. Try a meal, coffee, etc where you can actually talk. Movies can be both impersonal (no talking) and not an ideal first date.
But ask her. You are playing out scenarios in your head about what might happen but you don't know what will happen. Just go in, ask casually, and be ok with her saying no. If she does reject you determine if it is you, timing, etc but at least you will know and can either move forward or move on. Wait around and then you get to lament not asking her when some other guy does.
i'm sure you can get over a bit of awkwardness should she say no.
So what if she says no. Move on to the next.
Pick a specific activity you want to do which you think she might enjoy, then invite her to go do it with you. If you're going to go see a movie, go see a movie. Don't hinge your evening on her being there or not being there. My suggestion is; do the activity first, then get a meal after. That way if the conversation lulls, you can fall back on talking about what you just did.
Don't worry about "if" she will tell her friends. She will tell her friends. Most likely she will tell her friends while you're in the middle of doing whatever it is you're doing. If this freaks you out, wait until you're more serious with someone and then find out what she has been sharing with whoever will listen to her. For all the angst over boys and their locker room talk; it's nowhere near as invasive, personal, or graphic as what girls discuss with each other.
Maybe she doesn't want a boyfriend. It's ok to be casual and do fun stuff together. You really don't need to be serious all the time. If her friends start asking you questions about if you asked her out or went out or whatever else, say, "Why? Did you want to do something with me sometime?" There's a lot you can learn with that question.
Do I ask her out and risk the awkwardness or play it safe and just try and be friends?
Take the risk. Always take the risk. Right up until the point where you need to care about someone else more than you need to care about yourself, take the fucking risk. In whatever you do.
Just ask. A model in Maxim magazine once said something like "Want to know why we go out with jerks and gorillas? They asked, and you didn't." And forget being awkward around her and her friends. Why should you feel awkward for paying someone the compliment of asking her out? (Easier said than done, but I think that's the attitude to have.)
10-4 good buddy.
Especially were say a random game of dodgeball or something could break out. It should be fun. What was that class? F U N! Not a dinner then movie. Dinner is too high pressure you have to do the work of keeping things interesting, but the uncomfortable silence thing from "Pulp Fiction" can be used with amazing results. Movie, not physically involved first dates should be. Endorphins, blah, blah, blah, feel good, blah, blah, blah, come from physical activity. . .
Maybe go to a mall when all the crazies are there and make fun of them. . . toy store = play dodgeball and get kicked out. Try the thing from "Elf" and jump on the beds in a furniture store (I still have to try that) and get kicked out. . . whatever HAVE FUN!
Don't wait. The time will never be 'just right'.
Seriously, just ask her. If she says no, oh well, to bad. You will ask out many, many girls. You will get gunned down many times. This is not a bad or awkward thing to ask. Your asking her out on a date, not to be the third in a three way. The long term consequences are nil.