Bank of America offers a range of student banking products,with different minimum balance requirements. For instance, if you want to open a "CampusEdge" Checking account with bank of America, there would be no minimum balance requirement, and for saving account the minimum opening balance requirement would be $25.
I believe you do not need a minimum balance or deposit to open a student account with Bank of America (with the "CampusEdge" checking account option).
You can find more information and also, if you want to open one online, here.
You can find more information and also, if you want to open one online, here.