Both teams struggled to create anything in front of goal in the first half, but there was a let-off for the hosts in the 16th minute when Prince-Desir Gouano's attempted clearance rebounded against his own crossbar.
Liam Feeney should have put Bolton into the lead in the 70th minute when he collected a square pass from Ameobi in front of goal, but the Robins stopper pulled off an acrobatic save to preserve the stalemate.
City were dominant throughout the first half, but it was Bolton asking all of the questions after the break, and they nearly won it in the final minute when Ameobi's last-ditch header was saved.
The result leaves Bolton second-bottom of the Championship, four points behind today's opponents in 20th. body check tags ::