The result leaves Knights second in the table, two points adrift of leaders Ealing Trailfinders, who have two games in hand.
Victory avenged defeat in the reverse fixture but left Doncaster frustrated for a second successive weekend that they failed to collect a winning bonus point.
A tightly-contested first half saw few chances created. Referee Nick Wood was forced to police the scrums closely, with both sides penalised for early drives, standing up and not driving straight.
The home side finally broke the deadlock 10 minutes before half time when hooker George Roberts spun off the back of a strong driving maul, flicking the ball out to Billy McBryde to allow the fly-half to dive over. Alex Dolly added the conversion.
Knights went into the break a man down as Maliq Holden was sin-binned for an infringement near his own line.
As Holden returned early in the second period, Bedford lost a man of their own as prop Joe Conway was yellow-carded and Dolly slotted over the subsequent penalty.
Soon after, Steve Boden’s side bagged their second try as McBryde’s pass missed out two players, found Connor Edwards, who released centre partner Joe Margetts on a try-scoring run to the line. Dolly again improved the score.
With 10 minutes remaining, Dolly whipped out of the Knights defensive line to cleanly intercept a Bedford pass. On a turn, he fed McBryde with the Welshman running in the score, with Dolly again adding the extras.
Doncaster replacement Joe Wrafter was sent off for a high tackle against his former side in the last minute, as the Knights played out a man down.