The other white should connect to the white of the fixture. Connect the two white wires from the light fixture to the white wire located in the electrical box by twisting an orange wire nut onto all three wires.
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Install light fixture with 2 black and 2 white wires. You can wrap the wire around one of the screws that holds the fixture on but the only purpose it serves is to help hold the fixture up while you wire the black hot and white common wires. Never ever ever connect the ground wire to the white wire. Connect the lead wires from the fixture to the black hot wire in the electrical box by twisting a wire connector to the ends of the lead and hot wires. Then connect it to the supply ground wire of the junction box with a wire connector. Then push the connected wires into the junction box. Wrap the copper or silver ground wires from the light fixture around the ground screw.
The ground should be connected to the bare wires ground in the box. Connect the two black wires from the light fixture to the black wire from the electrical box the same way you connected the white wires. Bathroom lighting particularly light bars over a bathroom vanity often will have receptacles for two or more light bulbs. Repeat these connections with the two white. Never connect the fixtures ground wire to the white wire. In the course of replacing this light receptacle i came across two white wires.
How to install bathroom light fixtures with two black two white wires. You likely have a switch loop. You should find which one is hot when the switch is on mark it black with electrical taps and connect that one to the black wire of the fixture. Connect the black or red current wires and the white neutral wires. How do you find out which wire is hot or the black wire.