bathroom light fixture

Call an electrician.

Call Ceili

You can contact Electrician. I hope he will be help you.

Somewhere the grounded circuit conductor (white) is open. It may come from the switch box. You can check and see if the neutral is open at the fixture or switch box.
No! You should not use the fixture using the ground as a circuit conductor. This puts current on all the grounded surfaces and is a shock hazard.

If you are not knowledgeable with locating the open white conductor, call a qualified electrician and get it repaired.
Why is the fixture controlled by two switches and not just one???

2-way switching is not uncommon. You'd normally see it in a bedroom where there would be a light switch near the door, and one that can be reached from the bed. Why one in a bathroom? Maybe someone likes shitting in the dark.

More likely there's two entrances to the bathroom.