Don't feel bad about getting bit…she probably was sorry as soon as she realized what happened. Darting movements can garner such a reaction from any animal (and some humans) when they aren't used to contact.
Chasing a Basenji, even when you really need them to come to you (sometimes especially when you need them to come) quickly becomes a game and they will play tirelessly.
You could try a training exercise wherein you have really good cookies in your hand and call her just to give her a cookie. It won't take long for her to come to her name if she associates it with something good. Don't give up.