The 23-year-old, who has yet to play for Forest, will stay at Ashton Gate until January 2, subject to Football League clearance.
Head coach Sean O'Driscoll said: "Stephen's a young Irish winger who can play both sides, and someone who impressed when on trial at Forest during my time there and did enough to earn a contract.
"He's well-balanced, technically sound and got an eye for a goal. He's someone we think will add versatility and depth to the squad and that we can help to continue develop during his stay with us.
"We're very grateful to Forest for allowing us to take Stephen on loan."