Aimee Kelly’s first-half brace was complimented by second-half finishes from Heidi and Charlie Chadwick at a rain-soaked County Ground in Leyland.
There were two changes from the team that started against Norton & Stockton Ancients in the last round of this competition, with club captain Tilly Wilkes stepping in at left-back.
Kelly was given a starting berth in a new-look front three, flanked by Heidi and Danielle Maxwell as the wingers.
It was Kelly who had the first opening of the afternoon, but Bedford ‘keeper Nina Meollo stuck out an instinctive leg to steer the shot wide.
After Heidi had a snapshot straight at Meollo and Hartley glanced a header narrowly wide, Kelly struck twice in two minutes to give the Clarets control of the tie.
The first was a fantastic effort into the top right corner from 25 yards, and the second saw her latch onto a loose back pass to poke through the goalkeeper’s legs.
Real Bedford did have chances of their own, with Nicola Puddick and Chloe Logie both shooting narrowly wide.
However it was Burnley’s Brooke Cairns who came closest to notching the game’s third goal before the break, but her effort hit the post and bounced clear.
The visitors emerged from the dressing rooms with added impetus and Abbie Bensted was able to cut inside from the right, but her powerful effort was straight down Naoisha McAloon’s throat.
Burnley then got their third goal to put the result beyond any doubt on the hour. After a smart one-two with Kelly, Heidi confidently picked out the bottom right corner from seven yards.
Real Bedford weren’t giving up though, going straight down the other end and creating their best chance of the 90. After Beron Grant surged forwards, Logie couldn’t quite latch onto her cross.
Lou Roberts then turned to her bench for the first time, enforcing a change of formation with the introduction of Emma Siddall in place of Maddie Robinson.
Siddall later took aim from range and Cairns skewed an effort wide before Claudia Walker and Chadwick replaced Heidi and Kelly respectively.
The two substitutes combined for the fourth goal with 89 on the clock as Walker slid through Chadwick, and the number 19 scored her 10th goal of the season with a cool finish.
Roberts and co now wait the outcome of Monday night's FAWNL Cup last eight draw, before turning their attention to the visit of Derby County in the Northern Premier Division of the Women's National League on Sunday 16th November.
Burnley: McAloon, Heidi (Walker 83), Maxwell, Robinson (Siddall 65), Richards, Chandarana, McDaniel (Ravening 87), Cairns, Hartley, Wilkes, Kelly (Chadwick 83)
Unused Substitutes: Levell, Docherty, Paul
Real Bedford: Meollo, Puddick, Williams, Stovold, Bryant, Grant (O’Brien 83), Bensted (Hayes 75), Evans (Warren 68), Skyers (Byrom 75), Logie (Wood 68), Rush
Unused Substitutes: Herd, Fuggle
Goals: Kelly 23’, 24’, Heidi 60’, Chadwick 89’