The visitors had the best opportunity of the game to score three minutes before half-time but Nicola Sansone's bullet-like effort struck the crossbar with Bologna goalkeeper Gianluca Curci already beaten.
The result has left Sassuolo five points adrift of safety while Bologna are 17th and just two points clear of the relegation zone.
Sassuolo went into the game after a turbulent week, one that saw the club sack coach Alberto Malesani and recall former tactician Eusebio Di Francesco.
Having been dismissed in January and replaced by Malesani, Di Francesco demanded a strong performance from his players.
He got one and Sassuolo created the first chance in the 34th minute when Sansone's left-footed strike from the edge of the area was kept out by Curci.
The hosts' goalkeeper then breathed a big sigh of relief when he saw Sansone's attempt from outside the area crash off the woodwork in the 42nd minute.
Sassuolo picked up where they left off after the restart and, five minutes into the second half, the dangerous Sansone surged in the area but he slipped and fell to the ground with only Curci left to beat.
In the 73rd minute, Diego Farias released substitute Alessandro Longhi into the right side of the area but the defender sent his effort wide.
Bologna came to life with 13 minutes remaining and Lazaros Christodoulopoulos' cross-cum-shot deceived Sassuolo goalkeeper Gianluca Pegolo but flew just over the bar.
Pegolo made sure his team held on for a point five minutes from time when he kept out Christodoulopoulos's 12-yard strike.