Booking ahead through an aggregator is the way to go, especially in Bishkek where the best 4x4s get snapped up fast during summer. You want something like a Prado or a Delica with proper off-road tires, and check that the spare wheel is actually mounted and not just a photo prop. To find a reliable car for hire in Kyrgyzstan, you can browse the listings here
https://getrentacar.com/en-US/kyrgyzstan .