THE Reds missed the chance to leapfrog South Yorkshire rivals Sheffield United having been held to a goalless draw by Leyton Orient last night.
Barnsley, whose six-match winning run came to an end, still occupy the final play-off place thanks to Preston's 2-0 win over seventh-placed Peterborough.
Goalkeeper Adam Davies was in fine form and kept the struggling League One hosts at bay, while Conor Hourihane's 20-yard free kick was the closest Lee Johnson's side came to breaking the deadlock.
Substitute Milan Lalkovic was sent off late on for a two-footed tackle on Nathan Clarke, but honours were even as referee Gavin Ward brought an end to the match.
Lee Johnson, whose side remain unbeaten in seven and have conceded just once during that spell, said: "I'm pleased. I know you probably shouldn't say you're pleased with a point but I knew it'd be tough, so I have to say in the grand scheme of things it's a decent point."
Next up is a tasty clash at Oakwell against second-placed Preston on Saturday, before another big one at table-topping Bristol City.