Tips for biting?!?!

PLEASE HELP: my son is 2

We were over with friends when both of our kids started fighting over a toy and my son bit their daughter. I am shocked. He has never done that and I am so so upset. Normally a simple “no, no- take turns” will work and separate them. But he bit her and she bled. I feel like an awful mom. I’m embarrassed. I feel like it reflects my parenting. I don’t where he even learned to bite at. I immediately said no biting! That hurts! And then put him in timeout for 2 minutes. But I still feel awful. Any tips? Did I handle that situation right? What could I have done differently?