Kevin Lisbie and Jamie Cureton missed good opportunities to put the hosts ahead before Bowditch showed them the way after 37 minutes.
Impressive full-back Adam Smith swung in a cross from the right-hand side that was met on the volley by Bowditch from 15 yards out and his effort went over the head of goalkeeper Lee Butcher.
Two goals in six second-half minutes ended any hopes that Orient might have had of staging a fightback.
Bowditch slipped the ball to Smith down the right flank and he fired in a 30-yard shot that flew past a startled Butcher and into the roof of the net in the 57th minute.
Soon afterwards, Charlie MacDonald added to the keeper’s misery after Butcher could only parry an effort from Dean Lewington. The striker pounced on the loose ball and steered it into the net for his eighth goal of the season.