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.