Miles Rutherford and co went with the same starting XI that sent City top of the league with Ryan Peake, Jamie Horncastle, Connor Cody, Matt Axell and Scott Jones on the bench.
Gicu Iordache, on target against Cray Valley PM on Saturday, might have had a first half hat-trick. He had a shot cleared off the line in the 12th minute and then fired over some sixty seconds later when a smart pass from skipper Lloyd Rowlatt played him in.
Bridges’ keeper Kieron Thorp, who was outstanding, saved from Corey Heath five minutes later before Tom Tolfrey spurned a glorious chance at the other end.
Thorp palmed away a Josh Clack effort on the half hour before making another super save from Iordache to keep his side in the game.
Thorp’s counterpart Steve Mowthorpe got caught out in no man’s land and Tolfrey should have done better when Reece Price-Placid teed him up only for a couple of Chi defenders to hook his flick over the bar.
Tolfey made no mistake though with his penalty in the 41st minute, calmly slotting the ball away to Mowthorpe’s left.
Thorp did well to get something on Iordache’s drive just before the interval and was on hand again moments after the restart to deny Kaleem Haitham.
Jones replaced Jimmy Wild up top and went close with a couple of headers.
The hosts, who have scored twice in all five league games so far, couldn’t find a breakthrough against stubborn opposition.
Rowlatt had a shot charged down, Emmett Dunn headed narrowly over from a corner and Heath had a great chance to get Chi a point in time added on but dragged his attempt inches wide.
Chi face Three Bridges on another two occasions over the next couple of weeks in the FA Trophy and the group stages of the Velocity sponsored league cup.
Next up though is the FA Cup and a tough test against step 3 side Hartley Wintney in the second qualifying round of the world’s oldest knockout football competition on Saturday 21st September (Kick Off 3pm).
Chichester – Mowthorpe, Davidson, Hutchings, Dunn, Heath, Pashley, Clack,
Rowlatt, Wild, Iordache, Haitham, Subs: Peake, Horncastle, Cody, Axell, Jones