Wales international David Brooks gave the visitors the lead in the 28th minute. Good footwork from Brooks saw him beat debutant Jordi Osei-Tutu before firing into the top left corner.
However, Forest came out into the second half with a spring in their step. The Reds drew level after a delightful free-kick from Philip Zinckernagel was met by the head of Scott McKenna whose header was too powerful for Cherries 'keeper Mark Travers.
Chris Hughton's side were only level for 10 minutes. Good link-up play from the Bournemouth frontline saw Billing fire home past Brice Samba's near post.
Goalscorer Brooks was given his marching orders just two minutes later after picking up a needless second yellow card for dragging Osei-Tutu back on the counter attack.
Here is our warmdown of the game, where we go over the key talking points.
After the red card, Hughton decided to keep the same 11 players on the pitch, with Jack Colback and Ryan Yates at the base of the midfield. With the scoreline at 2-1 to the visitors and 30 minutes remaining, surely Hughton could've rolled the dice?
He decided to finally make a change in the 70th minute with Joe Lolley being replaced by Alex Mighten. Forest fans chanted for large spells throughout the second half, indicating they wanted Joao Carvalho on the pitch to change the game. Despite this, Hughton decided to make a substitution that was greeted with boos by the Forest faithful.
This was a talking point for many of the fans after the game, with many critising the substitutions made by Hughton. Still trailing, the expectation is to go on and try and rescue at least a point but the tactics being portrayed by the Reds boss showed nothing of the sort.
Carvalho finally entered the field in the 83rd minute, but by this point barely had any time to make a real impact on the game. Questions are starting to be asked of Hughton about his negative and often defensive football. More needs to be done in the middle of the park to progress the ball forward.
James Garner was perfect in that role last campaign and would be a welcomed addition to the CDM role which currently lacks forward momentum.
Lack of Forest tempo
The lack of tempo in the middle of the park for Forest was evident ever since the away side were reduced to 10 men. As you'd expect, Parker set his side up to have all his men behind the ball at all times to try and hold onto their one-goal lead, and credit to them they did it superbly.
With no real focal point for the Cherries, Tobias Figueiredo and goalscorer McKenna would often find themselves with the ball at their feet inside the Bournemouth half, reducing the need for two holding midfielders. The two centre-halves would feed the ball into Colback and Yates just for them to rotate the ball back to the defensive pair.
The only real-time Forest broke through was with wing-backs Osei-Tutu and Jordan Gabriel. The play through the thirds was too slow and could have been impacted better with the likes of Carvalho who try and play the ball forward at every opportunity.
Frustration was again evident at the full-time whistle, with a number of fans booing their disapproval of the performance once again.
Bournemouth's pressing game
This Bournemouth side may be made up of the same players as last campaign, but are completely different under new boss Scott Parker.
The former Fulham boss has instilled a "non-stop press" mentality into his side, which caused Forest all sorts of problems on Trentside.
Dominic Solanke, Brooks and youngster Jaidon Anthony never gave the Reds backline a chance to play out from the back, pinning them in their own half at every opportunity.
Anthony in particular was very effective down the left-hand side. His defensive ability for a young winger is top drawer. Combining that with his pace and talent on the ball gives Parker a great option should Arnaut Danjuma leaves the club this window.
The midfield trio of Emiliano Marcondes, Billing and Gavin Kilkenny dominated throughout. Brennan Johnson, who was the star for Forest last time out, was barely given time on the ball to produce the quality he demonstrated against Coventry City last weekend.
The Cherries deserved all three points from this encounter, and with the likes of Jefferson Lerma, Danjuma, Adam Smith, Steve Cook, Ben Pearson and Junior Stanislas yet to come back, they could well find themselves in a very good position come May.