Valley made it nine wins out of ten in all competitions with a relatively comfortable win at Birds Close.
The damage was done in the first half of the game, with a David Kolodynski double and a third strike in four games from Luke English easing Town into a three goal advantage by the interval.
Daniel Porter did grab a consolation just past the hour mark for the hosts, but Rugby remained relatively untroubled thereafter and could have easily added to their tally ahead of the game's conclusion.
Dylan Parker started for Town in place of the injured Omar Recci, and the visitors looked threatening from the off with Kolodynski volleying over the bar in the early minutes.
Parker also put one wide after Kolodynski's effort had been blocked, but Rugby did not have to wait too long to open the scoring when Danico Johnson's ball across the face of the goal was tapped home by Kolodynski on twelve minutes.
James Hancocks blazed one way off-target, before Kolodynski made it two with another cool finish after Johnson had again split open the Bugbrooke with his quick feet in the box - only to see his shot parried by home keeper Jake Bull into the path of Rugby's top scorer.
Joel Gyasi then steered the ball over from a Bugbrooke corner by Calvin Green, but Town were soon back on the offensive again with Danico Johnson chipping one high of the frame from the edge of the penalty area, before the same player smashed another strike just wide of the post.
The game was all but put to bed in first half stoppage time, when English powered home with his left foot after Edwin Ahenkorah had drawn a fine save from Bull.
Bull was back in the action early into the new period, pulling off decent stops to strikes from Caine Elliott and then Parker, but generally the visitors were a little less dominant after the restart.
Danico Johnson did nearly extend the lead further though when he guided the ball wide after Kolodynski, Ahenkorah and Max Johnson had all combined well to set up the opening for him.
However Bugbrooke grabbed themselves a slight lifeline when Ashley Bodycote could only punch a Green free-kick from deep into the body of Porter and the ball fortuitously rebounded back off him and into the net.
Bodycote redeemed himself shortly after with a full length save to Green's strike from twenty yards to help avert any prospect of a nervy final twenty minutes or so, with Rugby then missing a number of good opportunities to put the game out of the hosts' sight once more.
Substitute Adam Shaw missed a decent chance to open his Rugby account with virtually his first touch for his new club, whilst Ahenkorah put one straight at Bull from a dangerous position.
Green had two further chances for Bugbrooke, the first of which Bodycote beat away in unconventional fashion with his body.
Shaw again went close with his effort after he had barged his way past a couple of defenders to create himself space in the box, with Parker also shooting wide after Max Johnson had done well in setting him up ahead of the final whistle.
Valley Line-up: Bodycote; English, Hancocks, Loyiso Recci, Rosser; Elliott, Parker, Max Johnson; Ahenkorah, Danico Johnson, Kolodynski (Shaw). Subs not used: Fitzharris, White, Marsden, Lock. Booked: Hancocks.
Bugbrooke line-up: Bull, Whaler, Field, Caton, Avery, Green, Gyasi, Tamakloe, Porter, Power, Weatherly. Subs: Walton, Webster, Drinkwater, Binder.