Rural homestay relatively near to Bishkek?

At the end of a long trip through Russia and Kazakhstan I'm planning to fly out of Bishkek. Unfortunately I won't have a lot of time to play with in Kyrgyzstan: at the very maximum 4 nights. Ideally I'd like to spend one or two nights in Bishkek and then one or two nights in a rural homestay (best of all, a yurtstay). From what I can gather all the real untamed nature seems to be a bit far from Bishkek so I'll have to leave that for another trip, but I'm hoping there's something a bit tamer closer to hand. I'm primarily interested in a cultural experience, seeing Kyrgyz village or nomadic life somewhere I can do some relatively gentle day-hiking. Where's the best place to do this that isn't more than half a day from Bishkek by public transport?