Finally found a solution to our bathroom wiring nightmare!!! Thank you!!

One of the two pairs of wires goes to the switch. You have to figure
out which one. Best thing to do is to disconnect all the wires, turn on
the breaker, then CAREFULLY use a neon tester to see which wire pair is
"hot". This is the one that ISN'T the switch.

Then TURN THE BREAKER OFF AGAIN, connect the BLACK wire from the pair
you found to be hot to the WHITE wire of the other pair (the pair that
goes to the switch) with a wire nut. Then connect the remaining black
and white wires to the fixture.