Knights, who have now lost their last three league games, didn’t go home empty-handed, however, after sharing eight tries with the in-form home side who strengthened their grip on third place.
Denied victory by a late converted try in 25-25 draw at Castle Park in November, Knights hit the ground running.
A trademark big hit by Samoan No 8 Josh Tyrell forced a turnover which saw dual-registered full-back Cameron Cowell make a good run before being brought down in the Bedford 22 from where fly-half Simon Humberstone make good use of quickly recycled ball to put hooker David Nelson in with a long pass.
The Blues drew level two minutes later when full-back Rich Lane forced his way over from close range after Knights had come under pressure at a 5m scrum.
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Knights were soon back in front when scrum-half Tom James, who played for the Blues in the corresponding fixture last season, caught the home side flat-footed from a tap penalty in his own half before setting up the chance for centre Lesley Klim to break the line and then wrong-foot Lane to score near enough for fit-again Dougie Flockhart to make it 12-5.
The Scot also hit the target with a 17th minute penalty for a foul on James which resulted in a yellow card for Lee Dickson.
Not only did Knights fail to capitalise on their extra man after the penalty they also conceded ten points.
Lane linked up out wide to supply the finishing touches to an outstanding move in what was an entertaining game.
Will Hooley added the extras and levelled the scores at 15-all with a 25th minute penalty.
Bedford hit the front for the first time, despite messing up in the lineout when setting up for a catch-and-drive, when prop Tom Lindsay charged over for a converted try after they had regained possession.
Knights, who lost Nelson with a suspected shoulder injury, fell further behind just before the break when Hooley kicked a third penalty.
Just as in the first half, Knights were quick out of the blocks at the start of the second - James putting skipper Will Owen over for a try converted by Flockhart to make it 25-22.
Playing down the infamous slope, Knights got themselves back on level terms with a 53rd minute Flockhart penalty.
Bedford regained the lead when Knights were penalised for offside and Hooley again found the target.
The fly-half also tagged on the conversion after Jarrad Williams broke from an overthrown Doncaster lineout just inside their own half before sending Dixon over to secure his side a 35-25 lead at the start of the final quarter.
When Alex Shaw touched down for a fourth try on 75 minutes to secure Knights a bonus point it raised hopes of a dramatic late victory but their efforts were to end in disappointment.
Knights: Cowell, Flockhart, Klim, Owen, Lewis, Humberstone, James, Bergmanas, Nelson, Quigley, Challinor, Hicks, Hill, Ram, Tyrell. Rep: Langdon, Evans, Sproston, Civetta, Shaw, Heaney, Foley.