Kochkor has recently built a new taxi stand / bus station on the main road. There you can negotiate shared taxi rides to Bishkek, Naryn City, Balykchi, Cholpon Ata, Kara Kol, and sometimes At Bashi or Jumgal.
If you are looking for a cheap ride, try one of the minivan taxis also known as mashrutkas or if you have lots of time on your hands one of the buses that runs from Bishkek to At Bashi.
