Biting is totally normal at that age. Generally, they bite at school because they do not have the verbal skills to express their feelings. Some kids choose to hit instead of bite.
My son was the bitee (victim) for several months in his toddler class at pre-school. A classmate would just walk by and bite him for no reason. The child even bit my son when he was sitting in the teacher's lap one time. The biting got worse until most kids in the class were being bitten. The teachers, director and parent met several times to problem solve the issue. They tried keeping a teething ring on a necklace, keeping a teether lovie with the child at all times and finally, adding an adult aide to the classroom specifically attend to that child. Unfortunately, the problem continued and the child did have to be removed from class for about 3 months until they outgrew the biting.
While biting usually just bruises, biting can be serious. If the bite breaks the skin, you need to see your child's doctor. There is a great deal of bacteria in your mouth and it is possible to transfer bacterial infections and other diseases through a bite. The doctor will assess the bite and can prescribe antibotics if needed. This is straight from my doctor because the child bit my son and broke the skin once.
The school was right not to release information about the other child. This is standard practice and will continue as your child enters public or private school. The reason they do not give that information is to protect both children. The biter's parents were not giving your child's information either. While I'm sure you are a nice normal person, there are crazy people out there who might retaliate or harass you or your child. So it is for the safety of the children not to release names.
Also, I'm not sure why you had to sign a waiver. Typically you just receive an incident report. Actually you should ALWAYS receive an incident report when it happens, just like when your child gets a bump or bruise. It should tell you what happened and what first aid, if any was given. This can be important information for your doctor and plus, you just want to know when things happen, even if your kid is fine, it shows the care givers are paying attention.
Good news is that once the child gains verbal skills, the biting will stop and the screaming tantrums will begin *wink*. If the biting doesn't stop at that point, it might be necessary to remove the child from other kids for a while and see your child's doctor for some assistance. It can be very discouraging for parents because it is not like you told your kid to bite other kids at school, right?. . . Right? Kidding, but as they say, this too shall pass.