"We played very well,” BU boss Max Christie said. “From the start we played at a great tempo and were really at it.
"I thought we deserved the win. I think we are not far away from being a good side and we were very combative at Berwick and passed the ball well.
"It’s a long season and I’m sure we’ll come good.
"Our new signings Greg Skinner, Jamie McCormack, Danny Galbraith, Kieran MacAulay and Kyle Wilson are settling in well.
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"Our supporters want a team that plays with their hearts on their sleeves and in the last couple of games we’ve had that.”
The 1-0 success at Berwick followed a similar result for the BUs at Gretna 2008 on Saturday. Scorer Zander Miller also had a penalty saved.
“We should have scored four on Saturday,” Christie said. “We were 1-0 up, missed a penalty, hit the bar, hit the post and the game should have been put to bed a lot earlier.
"There is always a chance you can lose a goal from a setpiece or a mistake so it was never comfortable although we had all the ball.
"We passed the ball well at times and it was great to get the win after the week we’d had, losing to East Kilbride, Bonnyrigg and Spartans by the odd goal.”
Bo’ness, 11th in the table with 13 points from 11 games, have a home league game against East Stirlingshire this Saturday, KO 3pm.
Christie said: “We are looking forward to it. We know they are quite an established Lowland League club.
“So we’ll need to be right at it again on Saturday.
"Of course we want to be top half this season.
"But the big thing is we keep going, we stay together and we come in with a smile on our faces and a good attitude and see where it takes us.”
The BUs have landed an away tie against Wick Academy in the Scottish Cup first round on the weekend of September 18.