A lacklustre Blues side came away from Plainmoor with a goalless draw to set up a 3rd Round replay against The Gulls at St Andrew's later this month.
Manager Steve Bruce made numerous changes to the side that had beaten Wigan last week most notably with his son Alex included in a first team game for the first time since he joined the club almost a year ago.
The home side started brightly and looked to have taken the lead on seven minutes when Blues keeper Maik Taylor fumbled a cross under a challenge and Bedeau fired the ball into the net. Referee Keith Stroud had however already blown for a foul on the Blues keeper.
Blues then began to take control and Jermaine Pennant went close before Emile Heskey wasted a glorious chance to put Blues in front. The centre forward firing over the bar from six yards out with the goal at his mercy.
Walter Pandiani replaced Jiri Jarosik at the beginning of the second half but it was the hosts that probably deserved to break the deadlock.
Alex Lawless saw a 25-yard drive rebound off the crossbar just minutes after Taylor was forced into a save from the dangerous Bedeau.
Martin Taylor cleared off the line from Bedeau whilst his namesake pulled off further saves from Lawless, Kuffour, Hill and Lockwood.
Nicky Butt glanced a header just over the bar ten minutes from time whilst Julian Gray wasted another chance late in the second half.
The Gulls again went close to causing an upset however when Taylor was called upon to deny Connell with another fine stop in the dying minutes.
So Blues live to fight another day with a replay against the League Two side at St Andrew's which will probably be played on Tuesday 17th January.