Despite dominating possession for much of the game, and creating the best openings, Sunderland couldn't find the breakthrough.
Jozy Altidore and Ki Sung-Yueng were guilty of missing chances, but it was their inability to capitalise on some good openings that will disappoint boss Gus Poyet the most.
The Hammers, who stay just above the relegation zone after the stalemate, looked really toothless in attack, and aside from a few brief flashes of quality from Ravel Morrison, offered very little.
The home side really struggled to keep hold of the ball in the opening period, and when they did produce some slick build-up play, often through Mohamed Diame and Morrison, the final ball was not forthcoming.
Sunderland however played some excellent, intricate football, but their decision-making, at key times, let them down.
Altidore could have opened the scoring in the first few minutes, but his low effort was tipped wide by Jussi Jaaskelainen.
Bardsley thought he had broken the deadlock just after the half-hour mark, thundering a strike at goal from 30-yards, which beat Jaaskelainen, but cannoned back of the crossbar.
Sam Allardyce's men did come out after interval with added energy and impetus, but the same problems persisted.
Sunderland quickly regained control, and really should have broken the deadlock, but couldn't finish off several half chances.
Altidore was denied several times by Jaaskelainen, but he knows he should have done better.
The Finnish stopper had to be alert as the game entered the final 10 minutes, parrying well from a well-struck Ki effort from close-range, adding to the frustration on Poyet's face.
James Collins saw a header fly just wide in stoppage time, but it would been harsh on the visitors, who will feel with a little more quality, three points were there for the taking.