Chris Hughton named an unchanged side from the 3-0 win at Wycombe Wanderers last weekend with the only change coming on the substitutes' bench as the returning Lewis Grabban replaced Tyler Blackett for the game against his former employers.
The Reds made a sharp start to proceedings but they were almost undone by a short corner from Bournemouth on 11 minutes. Junior Stanislas took the corner and having got it back from Jack Wilshere, he curled a delightful effort inches wide of Brice Samba's far post with the Forest number one stranded.
Bournemouth were looking dangerous going forwards and they came close again moments later. Arnaut Danjuma got to the byline and delivered a cross to the far post but Shane Long could only loop a header up and over Samba's crossbar onto the roof of the Forest net.
It was proving to be an entertaining but even first half-hour at a bright City Ground and Forest were next to show when James Garner shifted the ball from his left foot to his right but drilled a low shot just wide of Asmir Begovic's goal from the edge of the Bournemouth penalty area.
The final act of a goalless first half saw Filip Krovinovic lash the ball wide from the edge of the box after getting on the end of a knock-down from Glenn Murray and Forest left the field fairly content with a first 45 minutes that saw them work extremely hard out of possession to give a talented Bournemouth side at bay.
The first 15 minutes of the second half were scrappy as both sides tried to make the first move in an attacking sense. Anthony Knockaert delivered a terrific free-kick into the centre of the Bournemouth penalty area which Joe Worrall flicked agonisingly wide but that was the only real opportunity of note in the early stages of the second half.
Still the chances remained at a premium for both teams as the game entered the final 15 minutes. Forest came close when Worrall sent an outstanding cross-field pass out to Knockaert but the Frenchman could only send his shot high, wide and into the seats in the Trent End.
Forest almost fashioned the opening goal they desperately craved with 11 minutes to play as Krovinovic sent a corner in from the left-hand side, the ball was met by Murray at the near post but his header from point-blank range was blocked on the line and Bournemouth were able to clear the ball away to safety.
Referee Chris Kavanagh only indicated two minutes of stoppage time at the end of the game, a sign of how the match had gone in many ways, but neither team could create that all-important opportunity to grab a winning goal and it ended in stalemate as the temperatures dipped further on Trentside.
Forest: Samba; Christie, Figueiredo, Worrall (c), Bong; Garner, Cafu; Knockaert, Krovinovic, Freeman; Murray
Subs not used: Smith, Ribeiro, Mbe Soh, Grabban, Colback, Jenkinson, Mighten, Lolley, Taylor
Bookings: Cafu 13', Freeman 46'
Bournemouth: Begovic; Smith, Carter-Vickers; S.Cook (c) (Kelly 5'), Rico; Wilshere (Brooks 66'), Pearson (Billing 82'), Lerma; Stanislas, Long (Surridge 81'), Danjuma
Subs not used: Travers, L.Cook, Kilkenny, Anthony, Zemura
Booking: Smith 45'
Referee: Chris Kavanagh