I have two bidets, neither use electricity. Also they fit on existing toilets. Just search bidet kit.

Don't need a heated bidet. We get -40C days here and I'll still take the ice-laser to the behind over TP.

They have battery operated ones! Maybe there's still an option for you there.

You only need electricity if you want heated water, I’d guess that a bidet comes with a tee fitting with a valve on the T side that goes in between the supply valve and toilet supply line, allowing the supply valve to provide water to both the toilet and bidet.