Good power, good outlet, dead outlet
If the voltage tester you are using is a "no-contact" or "glow stick" style tester they are not reliable beyond the presence of voltage. Induced voltages from nearby circtuits will cause these to glow.

By this I mean you need to test the circuit with another style of tester such as a solenoid style, LED, Neon or digital multimeter. Electricians for years have used the solenoid style because it puts a load on the circuit and induced voltages from nearby circtuits will not show up.

All that said, the outlets in the bathroom should not be on the same circtuit with your kitchen. If the house was built years ago this may be the case but it shouldn't be.

Step 1 double check that all your breakers are turned on. Some breakers don't appear tripped when they are and their handles only move to the center. Turn all breakers all the way off and then all the way back on.

Step 2 double check your wiring and make sure you are wired to the "Line" terminals on your GFCI receptacle NOT the "Load" terminals.

Step 3 if you have a GFCI receptable that is fed from another GFCI receptacle it cannot be coming from the "Load" terminals on the other GFCI.

Try some of that out and see what happens.

Good luck with your project!