First off, don’t refer to your child as ‘a biter.’ This is a normal—and temporary—way for young children to respond to feelings and situations they don’t know how to deal with properly. Adding a label causes you to see and respond to them differently, and it’s unwarranted. Excellent educators and caregivers are painstakingly careful not to do that to them at school and good parents don’t brand their children as well.
When you pick up your child from your child care center or school and hear from the teacher that they chomped a playmate, or you get handed that dreaded note, you’ll probably feel a little defensive. That’s normal. Don’t bother trying to explain how it was the other kid’s fault, or the teacher must have seen wrong, or some kind of alien was impersonating your darling little angel! Whatever excuse you come up with, any experienced teacher has heard it before. And I promise… as it slips out of your mouth and you hear it, it’s not going to sound nearly as convincing as you thought it would. Also, it’s unnecessary. As “un-fun” as this is for you, biting is a normal coping mechanism for younger children and doesn’t mean you’re a bad parent raising a monster. It’s not an attack on your or your family. It’s just a thing that happened.
Another well-meaning but misguided impulse that may come up is to call the other child’s parents and apologize. It won’t be helpful. Either they will understand that biting in small children is unfortunate but normal—in which case, your apology won’t be needed—or they will be feeling protective and respond… uh… less than diplomatically. Since you weren’t there, and they weren’t either, any conflict will just lead to hard feelings.
A last word of advice: don’t bother punishing your child when you get home. As you’re no doubt aware, small children have an incredibly short attention span, and probably won’t even connect the punishment with what they did earlier. You can talk about the right way for them to handle difficult situations in the future, but trying to punish them now will not help.