Sergeant Bergdahl has been allowed to go, with supervision, to a grocery store, restaurants, shopping centres and a library as part of the process of getting him comfortable with being out in public.
Sgt Bergdahl, 28, has been receiving care at Fort Sam Houston in San Antonio since returning to the US on June 13. He was initially treated at Brooke Army Medical Centre at the fort but was shifted last week to outpatient care at the military base.
He was freed by the Taliban on May 31 in a deal struck by the Obama administration in which five senior Taliban officials were released from detention at Guantanamo Bay, Cuba.
Sgt Bergdahl had disappeared from his post in Paktika province in eastern Afghanistan on June 30, 2009. Some former members of his unit have said he left of his own accord.
He has not commented publicly on the circumstances of his disappearance and the military has made no charges against him.
The army has said it is investigating Sgt Bergdahl's disappearance and capture, but investigators will not interview him until doctors give them the go-ahead.