Electrical Outlet not working - Open Neutral
Your testing is indicating that somewhere in that circuit the neutral for the one receptacle not working has become disconnected at a junction which is not in either location or the receptacles in your bathroom come from two different circuits.

To find it, you are going to need another method of testing. I would suggest a voltmeter.

First test your receptacle not working to verify that you have 120V between the hot and the ground. Then turn off the circuit to the receptacle that is working. Test to see if both receptacles are reading "0" to the ground. This will verify the receptacles are on the same circuit.

Now you have to find where both of these neutrals are connected together and that is where you will find the problem. Since you have turned the circuit off, verify all of the devices and lights connected to that circuit. Begin by opening the devices and lights closest to the receptacle not working and work your way back to the panel. 

The bad news is that the loose neutral may not be in one of these boxes. It may be in a junction box in either the attic or underfloor in a crawl space. The worst situation is that it may be in a junction box that was covered up and is now in a wall or ceiling and not exposed. This is why there is a code rule that all junction boxes must be exposed since they need to be accessible to perform maintenance on the conductor splices.

Let's just hope the electrician working on you dwelling was following the rules.

Good luck and stay safe. Remember you are testing areas where certain conductors are hot and make sure they are all deenergized before performing any repairs. If you have multiple circuits sharing boxes (e.g., receptacles wired through the same junction box as lights that are on a different circuit) then you may have live wires where you don't expect them. A non-contact tester can be useful as an extra safety measure.

P.S., since you are working on bathroom receptacles you might want to install GFCI protection on them before buttoning everything up. Unless they are already protected at an upstream receptacle or at the panel.