In my bathroom I have plug that has both white and black hot wire. What is the problem?

Can only guess with limited info and not sure what you are calling a "plug". If it is actually wires in a junction type box, it is possibly a black hot wire and a white switch leg (maybe with a section of black tape around the white wire to indicate that it also a hot wire).

If you are measuring voltage, you will get 120 between black and white, between black and ground and 0 between white and ground. Is this what you are measuring?

Where are you located?

Have you measured the voltage? What is the voltage?

How are you determining the black and white is hot?