It was the development squad's second consecutive loss following their 3-0 defeat at Harrogate at the weekend.
The match at Irongate was one of contrasting halves as far as Rovers were concerned, dominant in the opening 45 but without a deserved goal, whereas the second period saw the home side take control, scoring the only goal of the game.
Eric Kinder's side started brightly, Tim Payne firing over after just five minutes following good work from the lively Devarn Green.
A minute later Green himself tested the Brig back line but his effort was well saved by Lee Dovey.
Rovers continued to press, trialist Patrick Antelmi saw a point-blank header palmed away before Hugo Fernandez looped a header over from Raheem Hanley's cross.
Chances came and went as Antelmi curled an effort just wide, then Anthony O'Connor struck the woodwork from Payne's cut back.
All those missed chances came back to haunt Rovers as Bamber Bridge started the second half much the stronger of the two sides, taking the lead on 54 minutes.
Pressure in the Rovers area eventually told and striker Greg Johnstone fired home past Matty Urwin.
The Rovers 'keeper was called upon moments later, making a fine save to deny Alistair Waddecar.
Despite having all the momentum in the first half, Rovers struggled to carve open any clear cut chances in the second.
Substitute Paulo Jorge fired straight at the goalkeeper when well placed, Tim Payne hit an effort across goal before the last action of the match saw Antelmi shoot into the side netting from a tight angle.
The Under-21s are back in action next Tuesday when they face Chorley at Victory Park. Kick-off is 7.45pm.