Bury boss Alan Knill has been working tirelessly to bring in another forward to put pressure on Bishop and strike partner Glynn Hurst.
Morrell was in the stands after signing a two-year deal from Blackpool but may find it difficult to get in the side as Bishop provided the perfect response - firing home the game's only goal in the 42nd minute.
Morrell, who turns 34 this month, has scored 78 goals at Wrexham, Coventry and Blackpool, and Knill could not hide his delight at luring him to drop down two divisions.
"It's a real coup for us," said Knill. "He had plenty of other offers in our division and he could have stayed in the Championship.
"He believes in what we're trying to do so we're delighted a Championship player has decided to come to us.
"If any team in this division signed Andy Morrell it would be a decent signing so it's a great effort from the club.
Proven
"He's a proven goalscorer that's played at a really good level and still could play at that level but he's chosen to come to us.
"I have to say, though, it isn't because we've thrown the most money at him - it's because he wants to be part of what we're trying to do here.
"We were after more competition up front and were looking at a youngster on loan but this one came up and we thought, `let's go for it'."
Bury weathered an early storm before earning a deserved victory, with Hurst hitting a post late on.
"Brentford started brightly and we could have been 2-0 down after 15 minutes," added Knill.
"But after that I thought we were pretty good. We stayed strong and could have won by more but we'll take 1-0."
BURY: Brown 7; Scott 6 (Cresswell 90), Futcher 7, Sodje 7, Buchanan 6; Bennett 8, Dawson 7, Barry-Murphy 7, Jones 7 (Racchi 90); Bishop 7, Hurst 7 (Baker 83). Not used: Rouse, Belford.
Tweet
