The Old Lady picked up the lead in the first half via Mirko Vucinic, but they were unable to collect the three points as Daniele Portanoca equalised after Juve went down to 10
Mirko Vucinic opened the scoring around the half-hour mark, but was dismissed in the closing stages of the first half, and Daniele Portanova then restored parity after the interval.
Juventus dominated proceedings right from the start and had a number of chances to open the scoring as Milos Krasic and Vucinic inparticular looked lively early on. The Montenegro international tried his luck with a shot from 20 yards out after only seven minutes, but failed to trouble Jean-Francois Gillet.
Vucinic had more luck, though, as he escaped the attention of the Bologna defence after a free-kick from Andrea Pirlo and had no trouble breaking the deadlock with a low shot.
Krasic then created a good chance for Alessandro Del Piero as the experienced forward had the time and space to unleash a curled shot from the edge of the area, but his attempt went just wide of the upright. Krasic then came close to doubling his side's lead with a left footed shot from 20 yards out, but Gillet punched the ball clear with a good reflex block.
The home side were dealt a huge blow in the closing stages of the first half when they were reduced to 10 men. Vucinic went from hero to zero as he fouled Archimede Morleo inside the Bologna half and was consequently shown his second booking of the evening.
Juventus started the second half brightly despite being a man down and Krasic almost made it 2-0 only minutes after the break, but the former CSKA Moscow star fired just wide from a narrow angle.
Hardly 60 seconds later, Bologna restored parity after a set piece. Gaston Ramirez found Daniele Portanova from a corner kick and the defender headed home to level the scores.
Conte's men immediately took back the initiative and they could easily have grabbed the lead again. Both Pirlo and Giorgio Chiellini came close to adding their name to the scoresheet on the hour mark before Andrea Barzagli squandered two big chances to edge his team back ahead, and in the end the Turin side had to settle for a single point.
Juve resume match action on Sunday when they meet Catania in Sicily, while Bologna's next match is the home game against Inter on Saturday evening.