Henderson has joined the Cherries on a three-month deal and also made his first start in their 2-1 defeat to Leeds United.
Henderson has not made any first team appearances for the Hammers this season and has both Jussi Jaaskelainen and his new deputy Adrian ahead of him the pecking order at Upton Park.
Henderson spent last season on loan at Ipswich Town in the Sky Bet Championship, making 24 appearances.