Marcello Trotta came closest to ending the stalemate with a flurry of first-half efforts which were well saved by Saddlers goalkeeper Aaron McCarey.
Walsall, who had won six of their last eight, almost went behind on 17 minutes when Clayton Donaldson got ahead of his marker only to see his speculative volley bounce to safety off the upright.
The visitors always looked dangerous on the counter attack, with Fabian Brandy a constant threat.
Trotta again went close just before the break as his turn and volley forced a full-length save from McCarey as Walsall's goal led a charmed life.
But Dean Smith's side came into it more in the second half, Andy Taylor going close with a low drive and Bees keeper Simon Moore winning a one-on-one with Saddlers striker James Baxendale.
