cheaper slim one. https://www.amazon.com/Greenco-Non-Electric-Mechanical-Toilet-Attachment/dp/B01A17T3N6/ref=sr_1_16?keywords=%2415+bidet&qid=1578090016&s=hi&sr=1-16

if it turns into a problem in the winter you could just move this one to a non primary toilet since it's so cheap and buy a heated one for your primary toilet. For when it is definitely too chilly.

Greenco Bidet Fresh Water Spray Non-Electric Mechanical Bidet Toilet Seat Attachment

(I have no vested interest in any bidet company.)

I just figured out a solution for this a couple of days ago. I was trying to create a portable travel seat bidet. This set up is basically exactly what you're looking for.

From my previous post:

I purchased a portable camp shower that has a lithium battery pump....and connected the tube hose directly into a bidet (special one that i found on Amazon as well that takes a tube instead of a metal screw fitted hose). It fit and works absolutely perfectly! Hack the ends off the bidet that would normally be attached to the toilet and I can slide it into any toilet I am using. Put the water pump end into a portable water bucket and you're all set.

Links below:

Bidet: https://www.amazon.com/gp/aw/d/B01A17T3N6?psc=1&ref=ppx_pop_mob_b_asin_title

Shower pump: https://www.amazon.com/gp/aw/d/B092HSV2TR?psc=1&ref=ppx_pop_mob_b_asin_title

Portable water jug: https://www.amazon.com/gp/aw/d/B07MZR91ST?psc=1&ref=ppx_pop_mob_b_asin_title