usually when you're talking about attending school in that context you would use 'duduk' which technically means 'to sit' but it would be used like 'kamu duduk di sekolah'
"Kamu di sekolah" would translate to "You're at school". "Ada" in this context means to exist within, so, "You exist at school", which would then be more naturally "You are at school"
You would definitely exclude the "ada" 9 times out of 10, but having it is more formal.
(I hope this helps)