The Capital outfit go into tomorrow's quarter-final at East Peffermill buoyed by last month's 4-2 group-stage triumph at Newtown Park.
And although Ogunro admits BUs manager Max Christie was without some key personnel that day, he is confident his side have enough ammunition in their ranks to progress.
"We're really looking forward to the game, although we know it is going to be tough," Ogunro said. "We played each other in the group stages so it was a surprise to be drawn against them in the quarter-finals.
"We played well in that game and won comfortably, but they were missing some key players that day. We might be missing a few tomorrow so I'm expecting this one to be very different. Bo'ness had an excellent result against Spartans last week so they'll be confident. But it would be nice to continue our decent form in the competition and progress through to the last four. We have nothing to lose. We'll give it our all and hope we can get through, and then who knows, maybe the final."
Should the Uni bow out of the competition this weekend, it could turn out to be their last competitive fixture of the season despite still having one league game to fulfil. They are scheduled to play already relegated Vale of Leithen but no date has been confirmed.