Hillians boss Ian Chapman promised his players some hard work on the training ground after they failed to take the initiative against the bottom club, who played more than an hour with only 10 men.
Dean Carden was shown a straight red card on 27 minutes after the referee ruled he threw a punch at visiting skipper Darren Budd.
Despite struggling for survival, Bridges had the better of the first half, producing the majority of attacking play even if they were unable to put keeper Mark Zawadski under pressure.
Before the sending-off, Joel O’Hara had an appeal for a penalty turned down and late on Hassan Nyang was also denied by referee Kieron Bailey when he went down under challenge from Sam Fisk.
Marcus Elliott’s attempt on goal had the power taken out of it by a defender and went tamely through to Zawadski, while from a good move on the left, Elliott O’Hara got into a dangerous position but mishit his shot.
At the other end, Bridges’ keeper Jess Grimstone saved a powerful drive from a Pat Harding free-kick. The ball then fell to Max Howell, whose follow-up shot was ruled offside.
Stuart Tuck went close for the Hillians from a Budd free-kick and was then off-target from the edge of the area.
Not surprisingly Burgess Hill tried to make their numerical advantage count in the second half and enjoyed long periods of possession as they pushed forward.
However, the Bridges defence, led by skipper Ellis Hooper and Yaw Boeteng, who made his starting debut at right back, managed to deal with everything that came their way and kept scoring chances to a minimum.
Williams Peauroux cleared in the area as Harding failed to connect with a ball spilled by keeper Grimstone.
Kai Bichard was brought on in place of Max Howell, and Ryan Thompson replaced Karly Akehurst early in the second half. Bichard’s strike from a defensive slip-up was deflected wide and Tuck saw a free-kick from the edge of the area blocked as Bridges threw themselves at the ball to keep a clean sheet.
Hillians: Zawadski; Watts, Fisk, Budd, Phillips, Tuck, Tucknott, McLaughlin, Harding, Akehurst (Thompson, 57), Howell (Bichard, 53). Unused: Pointing, Cotton, Hayward.