The Old Lady picked up the lead in the first half via Mirko Vucinic, but they were unable to pick up the full three points as Daniele Portanoca equalised against ten man
Mirko Vucinic opened the scoring around the half-hour mark, but was dismissed in the closing stages of the first half. 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 Mirko Vucinic in particular 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 was able to break the deadlock after 30 minutes though, as he escaped the attention of the Bologna defence following a free kick, and had no trouble putting his side ahead with a low shot after being set up by Andrea Pirlo.
Some good play from Krasic then led to a 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.
Panagiotis Kone was the main dangerman for Bologna as the Greek midfielder caused Stephan Lichtsteiner a fair bit of trouble. The Tirana born winger was unlucky in his finishing though as he was denied by Buffon once, while two more attempts were deflected off the back of a defender.
The home side were dealt a huge blow in the closing stages of the first half when they were reduced to ten men. Vucinic went from hero to zero as he fouled Archimede Morleo inside the Bologna half, and was consequently shown his second yellow card of the evening.
Juventus started the second half brightly despite being one man down and Krasic almost made it 2-0 only minutes after the break. The former CSKA Moscow star aimed just wide though from a narrow angle.
However only sixty seconds later Bologna restored parity after a set piece, when Gaston Ramirez found Daniele Portanova from a corner kick and the defender headed home to make it 1-1.
Conte's men didn't seem to be too impressed though as they 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 score sheet at the hour mark before Andrea Barzagli got two big chances to make it 2-1, however, the Bologna goalkeeper proved to be too much of an obstacle as the game finished a draw.
Juve resume match action on Sunday when they meet Catania at Sicily. The Turin titans have collected seven points from three games following Wednesday's draw.
Bologna's next match is the home game against Inter on Saturday evening. The away side have picked up one point from three games.