The Honey Badger has been referred to by the Guinness Book of World Records as the most fearless animal in all of the animal kingdom. It really doesn't give a shit.
You sound like you are waiting for the girl to ask you out. If you're interested in someone, GO FOR IT. Who cares if you get shot down a bunch of times?
Here's what you do. You agree to hold her purse, but when she turns her back, start rummaging through it and search for a couple tampons. Then open them up and shove them up your nose. When she sees you, just act cool like nothing is out of the ordinary. She won't ask you to hold her purse ever again.