Signed on loan from Barnsley last week, Jarman was controversially sent off just before the half-time whistle.
Referee Tony Bates' decision incensed Bury manger Chris Casper so much he confronted the official on the pitch before half-time.
And in the second half Casper had to watch from the stand alongside the supporters as his team battled in vain to pull the match out of the fire.
Later, still fuming, Casper said: "I thought it was a hasty sending off. The lad lunged in but it was not a straight tackle over the top.
"We will look at the video to see if we can get the card rescinded."
On the performance, Casper added: "We created an awful lot of chances in the second half and it shows we can do it but we've got to start the game a lot more positively in future."
Andy Parrish, preferred to Chris Brass, put through his own net in the 29th minute while Andy Kirk netted his nintth of the season after finishing off a four-man move in the 40th minute.
Despite a one-man deficit Bury created opportunities and both Allan Smart and Matthew Tipton should have scored.
"Thanks to a moment of brilliance and a moment of luck we got the job done," said manager Colin Calderwood. "But at 2-0 Bury were still in the game.
"Chris Doig made a fabulous tackle had it been an inch the wrong way it could have been a sending off and a penalty and 10 versus 10 for the last 30 minutes."