Owls forward Fernando Forestieri slipped at a crucial moment and blazed over from inside the six-yard box shortly after half-time.
Marco Matias saw his tame finish allow Prince-Desir Gouano to get back and scramble the ball off the line.
Gary Madine headed over for Bolton when Derik Osede nodded a Liam Feeney free-kick back across goal.
Wednesday made the brighter start but missed chances through Matias and Atdhe Nuhiu.
Matias again found himself clean through after a clever pass from Daniel Pudil, but goalkeeper Ben Amos smothered the ball as the Portuguese forward elected to try to round him rather than shoot.
A Feeney corner was headed over by Osede as the hosts mounted their first meaningful attack, while at the other end Kieran Lee's brilliant skill to round two defenders was not matched by a tame shot, which Amos comfortably saved.
Forestieri spurned a golden chance two minutes after the restart when he lofted the ball over the bar after Nuhiu's header found him unmarked.
Substitute Stephen Dobbie finally forced Owls keeper Joe Wildsmith into a save, albeit a routine one, with a curling 20-yard effort in the 74th minute.
But although Bolton pressed late on they never looked like breaching Wednesday's defence.
Bolton manager Neil Lennon: "We're just lacking a bit of quality in the final third at times - the final pass or getting our shots off, but we've known that for a while.
"We're four games unbeaten, it's a clean sheet and another point, so I can take a lot of positives from it as well. We're not playing poorly. We're having a go and the players are giving me everything at the moment.
"My concern is that we're not taking chances. We need to find that little recipe to put teams away when we're in the ascendency and we haven't got that at the minute."
Sheffield Wednesday boss Carlos Carvalhal: "We drew but we missed a lot of chances - the first 10-15 minutes we could have scored two or three goals.
"Compared with the chances we had in the match, I'm not happy with the draw.  I'm happy with the dynamic of the team - it's hard work to create chances, but we didn't score.
"The story of the game was we missed a lot of chances, but that's football."
Bolton and Sheffield Wednesday shared a point in a goalless draw at the Macron Stadium.