We had talked briefly a few times prior to my approaching her.
So it wasn't completely out of the blue. I feel like this part is pretty critical. You had established yourself in a positive way before making the ask. If your first-ever interaction with her had been asking her out on a date, I doubt it would have gone as well.
In high school I was invited to be a third wheel for a friend who I'm pretty sure had never been on a date before. He was so nervous he ended up knocking over a large glass full of ice water. Twice.