Zemo planned on being tight-lipped about the whole ordeal. He didn't particularly care about what version of the story Bucky heard through the grapevine. There was always an ounce of truth and an ounce of fiction to every rumor, and his dear soldat could draw his own conclusions as to what he believed and what he didn't.
Either way, Zemo had no intention of throwing Elektra or Bobby under the bus. The baron took full accountability for his actions, regardless of who threw punches.
By now, Zemo had stripped down to his underwear and was preparing himself for the daunting task of figuring out which injuries were the worst. He had a feeling that gash on his arm might need stitches, but it was difficult to tell with all that blood clouding the wound. Only then did he realize that Bucky was still there and in that exact moment, Zemo truly did not have the energy to argue. So he let Bucky get to work with only a look of mild disapproval as protest.
"If you are going to insist on helping, can we talk about something else, at least?"