Get an outdoor-rated, thick gauge extension cord and plug it into a GFCI outlet. There is a teeny-tiny chance of electric shock during thunderstorms, but GFCI will shut the circuit quickly, usually. Consult an electrician before doing this. Or just get a GFCI outlet installed near the toilet. That's safer!
We thought about getting a bidet installed and two electricians said that the (maybe freshly revised?) code explicitly demands a new circuit. It cannot branch off a "countertop" outlet that is meant to feed a hair dryer or something.