Bowditch, who made his first league start only last Tuesday, took advantage of two howlers by Watford keeper Lenny Pidgeley, while his other strike was a classy finish.
Town went ahead after just five minutes when Pidgeley missed his kick and Bowditch tapped in.
There was little to choose between the teams in a lengthy quiet spell, before Bowditch struck again on 24 minutes, taking a Darren Bent pass on his chest and guiding the ball beyond Pidgeley.
Matt Elliott sent a strong header straight at Pidgeley before Heidar Helguson got in behind the Town defence only for home keeper Kelvin Davis to bravely block at his feet.
Chris Baird almost fed Helguson with a superb cross and Helguson then fired wide from a Scott Fitzgerald headed ball as Watford pressed.
They deservedly pulled a goal back in first-half stoppage time as Town failed to clear a Paul Devlin cross, and Fitzgerald turned to fire home.
Micah Hyde had a low shot held for Watford early in the second half while Bent shot just wide from an astute Bowditch pass.
Bowditch bagged his hat-trick on 61 minutes when Pidgeley and Jerel Ifil dithered over a long Davis clearance, allowing the England youth striker to nip in and slot into an empty net.
The game petered out somewhat after that, as Ipswich were happy to soak up the visitors' pressure and restrict them to hopeful long-range efforts.
Ipswich added the icing to the cake in stoppage time, Jermaine Wright firing into the corner of the net from 25 yards.