Crusaders had most of the chances in this first leg at Seaview but are now up against it if they are to make the semi-finals of the Setanta Cup.
They went closest early in the second half when a looping header by striker Jordan Owens was cleared off the line by big Bohs defender Evan McMillan.
Bohemians keeper Craig Sexton also made good saves to keep out efforts by Matthew Snoddy and Owens.
However, Dwayne Wilson went close to a late winner for Bohemians.
When Stuart Dallas slipped, Derek Prender pounced to deliver a low ball from the right but Wilson failed to apply a scoring touch at the far post and grateful home keeper Sean O'Neill was able to gather.
Bohemians manager Aaron Callaghan, a former title-winning player with the Crues, was ordered from the dug-out late on for comments made to match official Brian Turkington.