Evans, who had previously spent time at Leicester City before moving to Berkshire last summer, netted nine times for Peter Scott’s Under-21s.
He also made his first-team debut against Swindon Town in the EFL Trophy.
Last season, Reece spent time on loan in National League South with Torquay United, scoring twice in eight appearances as the Gulls lost out to Hornchurch in the play-off final.
Reading FC said: “We wish both Reece and Bedford Town all the very best for the upcoming season.”