Bulot struck both goals for mid-table Charlton, netting in the seventh and 38th minutes either side of a Michail Antonio equaliser, to earn his side a 2-1 win.
For Forest, the defeat was a setback to their slim hopes of a late play-off challenge, which had been fuelled by five wins in Dougie Freedman’s first six games since succeeding Stuart Pearce.
Both sides went into the game on the back of weekend victories, with Charlton beating Huddersfield 3-0 in front of their own fans while Forest were triumphing at Reading by the same scoreline.
Lawrie Wilson fired the first shot of the game after Karl Darlow had punched a free-kick away unconvincingly but the Forest goalkeeper was able to get behind the defender’s low drive.
Tony Watt was the man who had won the free-kick and he was soon hacked down again, with Jamaal Lascelles booked for the offence right on the D.
It was perfect for Bulot to try his luck and the midfielder’s effort was well-struck and perfectly placed, flying over the wall and giving Darlow no chance.
Antonio was guilty of a bad mis-kick as Forest retaliated but the winger made no mistake in the 14th minute when he cut inside from the left, eluded a couple of challengers and fired a low shot across Charlton goalkeeper Stephen Henderson and into the net to make it 1-1.
Forest captain Henri Lansbury was next to have a go but Henderson was comfortably behind his long-range effort.
Antonio caused problems again by cutting in from the left and it needed a header from virtually under the bar from home defender Alou Diarra to clear the danger at the expense of a corner.
Charlton had immense difficulty clearing that and Lansbury saw an effort from a tight angle flash across goal. Lansbury was involved in the next attack and ended up getting booked for a tussle with Diarra that left the Charlton man slumped against an advertising hoarding.
Forest were on top and Henderson allowed a low drive from Antonio to squirm past him, with the goalkeeper then punching unconvincingly from the resulting corner, which saw Lascelles head just wide.
Charlton’s reply was to retake the lead, with Bulot once more the scorer in the 38th minute. Watt sent Wilson racing into space on the right and his cross was despatched by the Gabon international.
Forest quickly picked up where they had left off and Henderson had to get down to parry a fierce long-ranger from Gary Gardner before the half-time whistle.
Charlton made two changes at the start of the second half as Wilson and Callum Harriott were replaced by Andre Bikey and Chris Eagles.
Joe Gomez forced Darlow into another save while the lively Antonio was well off-target at the other end before Matty Fryatt planted a free header over the Charlton bar.
Ben Osborn was only just wide with a long-range effort as Forest worked hard to find another equaliser in the knowledge that time was beginning to run out.
Chris Burke saw a shot blocked by the bulk of Bikey and Charlton had to scramble a corner away. The home side recovered its poise however and Yoni Buyens almost made sure six minutes from time only for Darlow to save his well-struck shot.
Darlow then did well to keep out Watt’s header but there was not enough time for Forest to get upfield in search of leveller.