Their winner tonight arrived against the run of play in the 58th minute when Bridges latched on to a loose ball and with Leicester defenders backing off the former Sunderland and Leeds star advanced to let fly with a 25-yard drive which rocketed into Paul Henderson's top right-hand corner.
It was his first goal for the club since arriving in a £350,000 move from Carlisle on transfer deadline day.
Although Leicester dominated much of the game they failed to make significant headway against a resolute Hull side whose defensive tactics included fielding two holding midfielders.
Leicester dominated early on but created just the one clear opening when the Hull defence could only half clear a Josh Low cross with the lively Levi Porter flashing a shot just wide from 12 yards.
On the half hour mark Boaz Myhill was Hull's saviour when he bravely blocked a Stephen Hughes' close-range effort.
Before the half-time whistle Leicester keeper Henderson had been called into action just the once on 37 minutes when he reacted well to beat away Nicky Forster's drive.
It was a similar story after the re-start with Leicester enjoying plenty of possession but failing to carve out decent chances.
They paid the price with that goal from Bridges just before the hour mark.
After falling behind there was plenty of huff and puff from Leicester, but little to show for their efforts.
On 75 minutes Matt Fryatt fired narrowly wide and then two minutes from the end the same player could only bundle a half chance into the arms of Myhill after Paddy McCarthy had miscued his shot.