How to splice the wires once the outlet has been removed, and it's not the last item in the circuit
It sounds like the load side of the GFCI receptacle in your kitchen was feeding your bathroom.  Assuming the colors were "normal" on the GFCI receptacle - a black and a white to the line side, another black and white on the load side - if this wasn't a bathroom, you might just splice the blacks with a wire nut, splice the whites with another wire nut, and re-energize.  

However, if you did that, you'd no longer have GFCI protection in your bathroom, which is a code requirement and an important safety measure.  You'd need to also replace your bathroom receptacles with GFCI receptacles to satisfy the code requirement.  

If you have more than one receptacle in the bathroom, you may be able to make the connections so that one new GFCI receptacle in the bathroom protects the other receptacles and / or the other power in the bathroom.  

Again make sure at a minimum your bathroom receptacles are protected by GFCI, it's not just a code requirement it's important for safety.