Bell joined Gateshead on a two-year deal in July.
Nineteen-year-old Bell was released by Sky Bet League One side Rochdale in June.
He put pen-to-paper on his first professional deal with the Dale a year ago, having made his bow for the first-team the season prior.
In total, Bell made three appearances for Rochdale at senior level, his first a cameo in a 1-0 win over Coventry City at Spotland.
He was loaned out to Evo-Stik Northern Premier League First Division North side Droylsden and Chester FC last season, figuring three times for the Blues in the National League between February and March.
Bell, who has yet to figure competitively for the Heed, could make his debut for Alty at Gainsborough Trinity tomorrow.