He has signed for the Shakers on non-contract terms, primarily as cover for first team goalie Glyn Garner.
Smith, the former Notts County keeper, played two games for Bury behind closed doors, against Blackburn Rovers and Wigan Athletic - and that was enough to impress Barrow.
"I'd seen Greg at Notts County and I know he's a good keeper," said Barrow. "We've only got a young lad in Peter Collins, so we always needed cover for Glyn in case he picked up an injury."
Smith, 20, was released by the Magpies at the end of last season after completing a three-year scholarship at Meadow Lane.
And Barrow is confident his new signing will get the chance to shine at Gigg Lane, if Garner does not maintain his fitness this season.
"Greg is a good keeper and Glyn's had a couple of scares already in the last couple of seasons," added Barrow.
"He's had a couple of thigh strains and Greg is just looking for the opportunity to play football.
"We have to bring in another goalkeeper because keeper Collins would have been thrown in at the deep end. As a young goalkeeper that is a big ask.
"Because we went into administration two years ago we are restricted who we can bring in, but it is important that we have strength and depth."
Barrow believes a smaller squad has led to a better atmosphere this year, as the Shakers look to contest a play-off place in Coke Cola Division Two.
"There's been a better atmosphere this year and I don't think there is a weak side in this division," said Barrow. "Ideally, we would like to bring in some more players , but we are restricted and have to work within those limitations."
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