the scentence on it's own doesn't really make sense so there are not a lot of answers, but 'tu y yo <em>vemos </em>el baño' is grammatically correct but I don't know who would use it considering it translates to you and I see the bathroom. because for it to be 'you and I go to the bathroom' inistead of 'el baño' it should be 'al baño' so 'tu y yo <em>vamos al</em> baño' if its not vemos or the question is formulated incorrectly I don't really know. But I hope I could be of help!
