But early goals from Andreas Weimann and Nahki Wells were ultimately enough to keep Dean Holden's side flying high in the Championship, with Luke Freeman's spectacular strike giving Forest hope, but not much more.
Forest might have taken the lead as new signing Nicholas Ioannou crossed brilliantly for Mighten, who connected powerfully with a header, only to see Bentley make a superb save.
It was Bristol City who were to break the deadlock with their first meaningful attack however, as two former Derby players combined.
Chris Martin cut the ball back from the right and found Weimann in acres of space 10 yards out, from where he was able to calmly guide the ball inside Brice Samba's left-hand post.
When Harry Arter's driven shot was spilt by Bentley, it looked for a second as though Lewis Grabban would bag an equaliser, but the ball would not drop for him amid a furious goalmouth melee.
And Forest were left with a mountain to climb in the 22nd minute, when Martin's second assist of the game – this time a header – set up Wells to find the back of the net with an acrobatic shot on the turn.
Forest had not scored a goal in their first three Championship games having inexplicably dropped out of the play-offs on the final day of last season, and the prospect of needing to score three to collect their first victory of the campaign felt unlikely.
But their first goal was not long in coming and, when it arrived, it was a spectacular way for Forest to break their duck, as former Robins player Freeman collected the ball just outside the box, before sending a rasping, unstoppable shot across goal and inside the far post.
Forest were suddenly back in it, with Grabban twice coming close with a low, deflected shot and a header from the resulting corner.
Arter drove a low shot well wide as Forest began their hunt for an equaliser after the break. Grabban headed a great chance wide following good work from Freeman.
Christie almost scored a fine individual goal after pushing forward from right back, riding two or three challenges and hitting a powerful long-range drive that Bentley kept out brilliantly.
Bentley made another crucial save as substitute Lyle Taylor hit a shot on the turn, which the keeper bravely smothered at his feet. Taylor flashed a shot across goal and wide as the clock ticked down.
Antoine Semenyo almost killed off the game in injury time for City, but Samba made a good save.