I had an infected finger amputated three days ago. When will my bandaged stump fully heal?

Yes it should. With appropriate antibiotic therapy and resection proximal to the infection, healing should proceed uneventfully.
Avg 1-2 wks. It is important for the infection to be properly treated for the wound to heal. If you are on proper antibiotics and doing daily wound care, it should heal in 1-2 weeks. Sometimes a secondary surgery is required if there is bone or tendon exposed in the wound.