Central defender Bischoff, who is on-loan from Manchester City, headed home his first goal for Wolves after 43 minutes to boost caretaker manager Stuart Gray's slim hopes of being handed the job as successor to Dave Jones on a permanent basis.
Kevin Cooper had given Wolves the lead from the penalty spot after 18 minutes only for David Johnson to equalise three minutes later.
Johnson's strike, his second in successive games, proved the highlight for struggling Forest who had their soon to be appointed new coach Mick Harford watching from the stands.
Forest have failed to win away from home all season and have now collected just five points from their last eight games - leaving them rooted in the bottom three and all geared up to fight a relegation battle.
Wolves have higher hopes of forcing their way into the promotion picture under the control of a new manager.
Former Romanian national boss Victor Piturca is the latest man to apply for the job.
Whoever is appointed will inherit a man in form in the shape of the impressive Cooper.
Cooper, who showed his liking for converting penalties against Derby County last month, once again proved clinical from the spot to fire Wolves ahead.
Referee Michael Ryan had little option but to point to the spot when Matthieu Louis-Jean pulled Carl Cort's shirt.
Cooper gave goalkeeper Paul Gerrard no chance from the resulting penalty with a powerfully struck drive.
But Wolves' lead proved to be short lived as Forest were quickly back on level terms.
Johnson owed his strike to some woeful Wolves defending when Andy Reid's corner created panic in the area.
The unmarked Michael Dawson headed the ball into the path of Johnson whose acrobatic overhead kick beat Michael Oakes at the near post.
Forest proved to be equally as ineffective at defending from set pieces and they were also undone by a corner when Wolves regained their advantage two minutes before half-time.
Seconds before Bischoff struck, Forest had a double let-off when Gerrard saved from Kenny Miller and Shaun Newton's follow-up twice bounced off the bar before being cleared for a corner.
It was from the resulting corner by Colin Cameron that Bischoff rose above the Forest defence to head home and seal Wolves' win.