Upvote:2
It does not appear that there are any direct buses, though it probably wouldn't hurt to pop in to the bus terminal in Popayán and ask. Failing that, the most straightforward route is to take a bus (7–8 hours) from Popayán to the border town of Ipiales, from which you can take a minibus or taxi to Tulcán, Ecuador, and from there a bus (about 4 hours) to Quito.
Upvote:2
This is quite a bump to an old thread, but it may serve someone.
There are buses leaving from Cali (they have to pass trhough Popayan, but I don't think they stop there) to Quito and Lima. The company name is Ormeño.
From Popayan to Cali is a relatively short ride (2 hours in a bus), and you can contact Ormeño at Cali's Terminal de Transportes. The contact information I could retrieve is this, I'm not sure if it's accurate as of today:
CALI
Dirección: Terminal de Transportes de Cali, Calle 30N Av. 2A 29, Local 200
Contacto: (2) 6617083 / (2) 6687868 - / 314 633 2436
Please remember that Colombia's country code is +57.