There are several bus companies operating this route.
Actually, the route starts from Athens and ends at Tirana. Korce is one of the stops.
In Athens, near Metaxourgio Metro Station, many bus companies are running the buses.
The price is Euro 30 for one way. 2 to 3 buses for each bus company each day. However, I would like to recommend you to call them up to reserve the seat or go there to buy tickets in advance.
Detail of route:
8 to 9 hours (Athens -> Korce)
Broader is Cristalopigi. It may take from 30 mins to 3 hours to complete the passport check. It depends on the number of buses at the customs. The bus driver will collect the passport from each passenger and once it is ready, the bus driver will give you back the passport.
Bus Company contact:
When I visited Albania in 1988, as only officials could use a (state) car, they were very few. The people, if they were wealthy enough used horse driven carts. On my recent visits,after 2000, I noticed that horse driven carts had been replaced by petrol powered cars and that the number of horse driven carts had dramatically fallen down . Actually, they are found now only in the villages and no more in towns. In some town, there are even road signs that forbid them.
Avenue Kiço Greço, next to the market minibuses or fourgons are standing. They will depart at the end of the market. There are minibuses both for the neighboring towns and villages and for long distance destination such as Tirana.
Buses are extremely decrepit, and only for the lowest of the low, like me. Everyone else gets a furgon (minibus - new, if you can wangle it) or a taxi.
One curiosity about buses between Athens and Korca is that they take much longer going to Greece than they do going in the other direction. The reason isn't, as you might think, Greek border formalities so much as the fact that Albanian passengers going to Greece insist on the bus going miles out of its way to drop them off at the place they're going to (Velestino, Lamia, Salonica, etc). In the other direction, of course, that doesn't happen, as realistically speaking there's only one road that buses CAN take.