2 year old biting

Hi so I need some advice..

My son bit a little girl today at the playground. I apologize to the mother of the girl for my son biting her and made sure she was ok. The moment it happen I told my son we were leaving and that biting was not ok. He threw a tantrum while we were leaving but while I was trying to gather our things I noticed the mom or grandma saying some rude things about my son and making faces at me like I was a horrible mother but I didn’t say anything. This made me upset because I did apologized for the incident and told my son in front of her that what he had done was not ok.

While I was driving home I was thinking if I should’ve handled the situation in a different manner. I just want to get some opinions.

This is also the first time my son does this so I was in a bit of a shock when she yelled out that he bit her.