With several Ireland Under-20 players also unavailable, O'Donohoe partners Ian McKinley at half-back, Ian Madigan reverts to full-back in a lively looking back-three which includes Darren Hudson and Michael Keating.
Prop Jack McGrath, who has scored tries in each of the last two rounds, starts in the front row alongside Aaron Dundon and Simon Shawe.
Ed O'Donoghue has been named in the second row alongside Ciaran Ruddock, an older brother of Ireland international Rhys Ruddock.
Eoin Sheriff completes the back row with Paul Ryan and number 8 Leo Auva'a, who has been playing well for Division 1A leaders Old Belvedere.
Having qualified from Pool A in second place behind high-flying Worcester Warriors, Leinster face a tough tie away to Bedford, the second-placed English side who include, in their ranks, former Leinster player Brendan Burke.
Speaking ahead of the knockout clash, Leinster coach Colin McEntee said: "It has been a challenge this week with so many players away on Irish camp, Magners League preparation and Ireland Under-20 commitments, but that merely serves to hone our focus ahead of an exciting quarter-final.
"We've been delighted with the approach of the players this week despite our lack of preparation time and each of the players is determined to stake their claim.
"The British & Irish Cup is one of just three competitions that we compete in at the top level and so it's vital that we get off to a strong start and assert ourselves from the off."
"A lot of hard work has gone into qualifying out of our pool and the players don't want to let up now. To get out of a group with Worcester, Newport and the Cornish Pirates was no mean feat and the competition has gone from strength to strength again this year.
"The same levels of enthusiasm have been evident (this week) and I suppose that a lot of the panel can look to the likes of Andrew Conway, Ian Madigan, Jack McGrath and Ian McKinley for motivation as they have all benefited from senior game time in recent weeks.
"Encouragingly, the senior management have shown their indication to reward good form in this competition. But we face a massive test and we'll have to be sharp from the off.
"Bedford are a good side with a big forward unit. We have seen some of their footage this year and they're clearly a side who like to play with pace and tempo.
"They beat Ulster in the pool stages, finishing in top spot and in addition finished second in the league stage of the English Championship, so they're a team we have great respect for.
"But this week is, in essence, a cup final for us and we're just focused on our own performance. Saturday afternoon is about winning."
Click here for details of all four British & Irish Cup quarter-finals.
LEINSTER (v Bedford Blues): Ian Madigan; Darren Hudson, Daniel Riordan, Eamonn Sheridan, Michael Keating; Ian McKinley, Paul O'Donohoe (capt): Jack McGrath, Aaron Dundon, Simon Shawe, Ed O'Donoghue, Ciaran Ruddock, Eoin Sheriff, Paul Ryan, Leo Auva'a.
Replacements: Tom Sexton, Stewart Maguire, Michael Kearney, Jordi Murphy, John Cooney, Noel Reid, Colin O'Shea.