Marco Di Vaio put the visitors ahead in the 56th minute with Miralem Pjanic equalising for the Romans six minutes later.
Both sides then failed to take advantage of opportunities to earn a win in a lively encounter.
Roma went into the clash riding a four-match winning streak in the league but were looking to bounce back from their Coppa Italia elimination at the hands of Juventus in midweek.
They almost took the lead in the opening minute.
Aleandro Rosi fed captain Francesco Totti in the area but his eight-yard shot was kept out by Bologna goalkeeper Jean Francois Gillet.
Roma wasted a good chance before the half-hour mark when Totti served Fabio Borini in the box and he shot wide from a good angle.
Bologna then forced Roma goalkeeper Maarten Stekelenburg to make his first save as he cleared Gaby Mudingayi's drive from 30 yards.
Before half-time, Bologna's Andrea Raggi should have done better than strike Alessandro Diamanti's cross wide from just six yards.
The visitors continued to press forward and were rewarded before the hour mark.
On a fast counter-attack, Di Vaio surged inside the area and coolly struck the ball past Stekelenburg.
Bologna's joy was shortlived, however, as Roma restored parity when Pjanic curled a free-kick towards the far post and beat Gillet.
Bologna almost regained the lead two minutes later but Stekelenburg kept out Di Vaio's goal-bound effort.
Gillet then made a good save to clear substitute Bojan's 12-yard shot in a frantic end to the contest.
With six minutes remaining, Bologna almost got the winner but Henry Gimenez's header from Archimede Morleo's cross went just wide.