Flights run frequently between Bishkek and Osh, often more than once a day. We booked for both journeys the day before.
Osh airport is wonderful. The check in hall serves coffee - wow!. The departure hall is a roof over a tarmac where you can watch your luggage being loaded a few metres away. I thought Osh was hot but it was nothing compared to sitting in a Yak 40 with no aircon. Delightful moments: the luggage racks full of melons in special carriers; getting served sweets by a sweaty air hostess (why should she be different to us?); drinking cold drink out of disposable cups; on landing being asked to remain seated until the crew have left the aircraft!
Very cheap, and arranged by our hotel. We used taxis to get us to the airport, but in and around Osh it was foot power or a minibus from our tourist agency. There was no hairy driving, and we loved the carpeted seats.