Hendy's quickfire double and an Angus Scott-Young score had put the black, green and gold in control at the break, despite two tries from Pat Tapley for the Blues.
But both sides made a huge amount of changes at half-time and it was Bedford who bossed the second half, scoring three further tries to get the job done.
The impressive Henry Pollock was able to add to Saints' tally with a try of his own, but Bedford bagged the victory.
Saints will now look forward to their second and final pre-season fixture, at home to the Barbarians next Saturday.
Phil Dowson's team, which included four guest players and three loanees, had headed to Goldington Road looking to blow off some cobwebs.
But it was Bedford who made the stronger start to the match, pliling the pressure on Saints.
And eventually the reward came as wing Tapley overpowered scrum-half Archie McParland out wide to grab the first score of the game.
Will Maisey converted from the touchline to make it 7-0.
Saints lost Joel Matavesi to injury before they eventually responded, using a scrum penalty to set up field position, allowing James Grayson to send Hendy in for a score out wide.
Grayson saw his conversion rebound off the left post to leave the deficit at two points, but Saints were soon ahead as Hendy scored his second in quick succession.
Bedford failed to deal with a McParland box kick and after the ball bounced loose, Hendy showed good awareness to get there first, gathering before sprinting in for the try.
Grayson made no mistake with the conversion this time, and Saints were 12-7 up.
The away side were starting to call the tune, and the third score arrived when Reuben Logan picked a tidy line before bursting through and offloading to the onrushing Scott-Young.
Grayson converted again, but Bedford responded before the break, using a 50:22 to get into Saints territory before Matt Worley showcased his fast footwork to send Tapley in again on the right.
Maisey missed the conversion and Saints threatened to issue a rapid riposte but a knock-on thwarted their progress to leave the gap at seven points at half-time.
Both sides made a raft of changes at the break, with Saints introducing the likes of Toby Fricker and Jake Garside.
The black, green and gold did well to repel a home charge from a rolling maul, turning the ball over and then winning a free-kick from the resulting scrum.
But Bedford kept coming and after some strong counter-rucking they won a penalty, which allowed them to kick to the corner and rumble over through Jacob Fields.
Louis Grimoldby converted to level the scores and Bedford were now looking like the most threatening side, with the likes of Dean Adamson and Worley starting to stretch Saints.
Worley soon went over for a deserved try to put the Blues ahead, and Grimoldby added the extras.
Former Bristol Bears wing Toby Fricker then had to do some excellent cover work for Saints after a fine through ball from Jack Arthur threatened to find Sean French.
The Blues looked likely to add to their lead, but it was Saints who scored next as some special footwork and awareness from Garside opened the door for Pollock to dot down.
Matty Arden missed the conversion to leave the gap at two points as the clock ticked towards the final 10 minutes.
And Bedford finished the job as Luke Frost displayed real desire to dive over the line.
Grimoldby again converted to ensure Saints suffered a nine-point defeat.
Bedford Blues: Worley; Tapley, Grayson, Venter, Adamson; Maisey, Lennon; Jack, Fish (c), O'Connor; Williams, Woolford; Arthur, Curran, Howard.
Replacements: Conway, Fields, Heffernan, Onojaife, Frost, King, Day, Grimoldby, French, Coulson.
Saints: Hendy (Grayson 60); Glister (Daniel 40), Litchfield (Arden 37), J Matavesi (Baker 12 (Fricker 40)), Seabrook (Litchfield 60); Grayson (Garside 40), McParland; Green (Patten 54), Cruse (c) (Wright 40), Millar Mills (Prowse 35); Atuanya (Vukasinovic 35), Scott-Young; Logan (Moore-Aiono 40), Cherry, Pollock.
Referee: Joe James