...but it takes a some time.
There is no fast way from kochkor to osh. You are looking at atleast a full day. You have 3 choices:
Via bishkek - most simple, lots of mashrutkas, may be quickest. (If I just wanted to get between the 2 quickly and cheaply I would take this option).
Via kazarman - more complicated in that afaik you still need private jeep for at least some of the journey. I would only recommend this way if you have the time and inclination to make the most of kazarman (i.e. saimaluu tash visit).
Via Sussamyr valley - no public transport so requires private car/hitchhiking. Even though it's shorter than going via bishkek the road is bad so may not be much difference in time. If you want some nice hiking around kyzyl oi it can be a good option.

