The Egyptian sent an early header crashing against the woodwork and Stephan El Shaarawy's headed goal from the rebound was ruled offside to signal a frustrating evening for the hosts.
Salah was unlucky again in the 23rd minute when he broke clear and hit the inside of the far post with an angled drive and then had his effort from the rebound saved by Bologna goalkeeper Antonio Mirante.
Almost immediately Luca Rossettini added insult to injury when he scored against the run of play for Bologna with a header that slipped through Roma goalkeeper Wojciech Szczesny's hands.
Salah curled another effort against the post at the start of the second half after Roma coach Luciano Spalletti had brought on veteran playmaker Francesco Totti for a rare appearance.
The 39-year-old's presence appeared to inspire Roma and he set up the equaliser with a through ball that Salah sidefooted past Mirante.
Roma dominated the rest of the game, with Totti at the centre of the action, but could not find a winner as they dropped six points behind second-placed Napoli.
The top two teams qualify for next season's Champions League group stage while third place earns a spot in the final qualifying round.
(Writing by Brian Homewood; Editing by Tony Jimenez)
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