“Teacher,____ go to the washroom?

The correct answer is: May I

If someone is asking for permission, the person can use 'may I?' Because, the other person may or may not allow to do the thing. By asking politely, we can satisfy our needs. Here, the girl is asking for washroom and so she uses 'may I' and the teacher will allow or will not allow. But most probably the teacher will allow since she asked politely.