So what do we actually know about this encounter. It wasn't an actual debate, but occurred during the 1860 meeting of the British Association for the Advancement of Science that was held in the newly constructed Oxford Science Museum. It occurred during a discussion period following a paper by John Draper entitled “Darwinism and Human Society.” There had been great public interest in Darwin's “On the Origin of Species” that was published 8 months prior to the meeting. A large crowd of more than 700 had assembled since it was rumored that Samuel Wilberforce, a well known public speaker, would present a rebuttal to Darwin's ideas at this meeting. There was no written proceedings of this meeting so we must rely on outside sources for any information on what actually happened. There were two journalistic accounts of the meeting. Neither of these articles mentioned the Bishop's question to Huxley. The following is a portion of one of the journalist's account that appeared in the Athenaeum 
Yet the main interest of the week has unquestionably centred in the Sections, where the intellectual activities have sometimes breathed over the courtesies of life like a sou'wester, cresting the waves of conversation with white and brilliant foam. The flash, and play, and collisions in these sections have been as interesting and amusing to the audiences as the Battle at Farnborough or the Volunteer Review to the general British Public. The Bishop of Oxford has been famous in these intellectual contests, but Dr Whewell, Lord Talbot de Malahide, Prof. Sedgwick , Mr Crawford , and Prof. Huxley have each found foemen worth of their steel, and have made their charges and countercharges very much to their own satisfaction and the delight of their respective friends. The chief cause of contention has been the new theory of the Development of Species by Natural Selection — a theory open — like the Zoological Gardens (from a particular cage in which it draws so many laughable illustrations) to a good deal of personal quizzing, without, however, seriously crippling the usefulness of the physiological investigation on which it rests. The Bishop of Oxford came out strongly against a theory which holds it possible that man may be descended from an ape — in which protest he is sustained by Prof. Owen, Sir Benjamin Brodie, Dr Daubeny, and the most eminent naturalists assembled at Oxford. But others — conspicuous among them Prof. Huxley — have expressed their willingness to accept, for themselves as well as for their friends and enemies, all actual truths, even the last humiliating truth of a pedigree not registered in the Herald's College. The dispute has at least made Oxford uncommonly lively during the week.
It appears that it was a lively discussion with both sides skillfully presenting their arguments to the delight of their followers. If Wilberforce did put a question to Huxley concerning his ancestral preference and Huxley did make a witty reply, it didn't seem that the journalists present took much notice.
There were several letters, written shortly after the meeting, that provide some hints on what actually took place. The first was a letter written by Joseph Hooker, the Assistant Director of the Kew gardens, to Darwin on July 2, 1860. He wrote the following
Well, Sam Oxon got up and spouted for half an hour with inimitable spirit, ugliness and emptiness and unfairness … Huxley answered admirably and turned the tables, but he could not throw his voice over so large an assembly, nor command the audience; and he did not allude to Sam's weak points nor put the matter in a form or way that carried the audience. The battle waxed hot. Lady Brewster fainted, the excitement increased as others spoke; my blood boiled, I felt myself a dastard; now I saw my advantage; I swore to myself that I would smite that Amalekite, Sam, hip and thigh if my heart jumped out of my mouth, and I handed my name up to the President (Henslow) as ready to throw down the gauntlet … Then I smashed him amid rounds of applause.
It is obvious that Hooker thought that he was the champion of the day. He didn't think that Huxley got through to the audience.
A second letter was from John Richard Green to Sir William Boyd on July 3, 1860. Commenting on Wilberforce he said
Up rose Wilberforce and proceeded to act as the Smasher. The white chokers (clergymen) who were present cheered lustily … as Samuel rattled on — He had been told that Professor Huxley had said that he didn't see that it mattered much to a man whether his grandfather was an ape or no! — Let the learned Professor speak for himself' and the like.
and commenting on Huxley he said
Huxley — young, cool, quiet, sarcastic, scientific in fact and in treatment gave his Lordship such a smashing … This was the exordium ‘I asserted, and I repeat, that a man has no reason to be ashamed of having an ape for a grandfather. If there were an ancestor whom I should feel shame in recalling, it would rather be a man, a man of restless and versatile intellect, who, not content with an equivocal success in his own sphere of activity, plunges into scientific questions with which he has no real acquaintance, only to obscure them by an aimless rhetoric, and distract the attention of the hearers from the real point at issue by eloquent digressions and skilled appeals to religious prejudice.’