Indeed yes, madam, I said; I'm the director.
"In that case, I wish you to help me with an important project. It is imperative that I contact one of the people who are performing at the weekend. You must help me meet him - er, them."
Who, I asked, are you? She drew herself up to Boadicean proportions. "My name," she said grandly, "is Councillor Mrs Jane Tweedale. I'm on the local council. It is of the utmost importance that I get to meet Mr Jeremy Paxman in private on Sunday, in order to discuss a matter of great urgency".
And what would that be? Corruption in the municipal chamber? Housing initiatives? Falling school attendances? Her eyes gleamed with love. "Oh, she sighed, "I just want to meet him."
Madam, I said coldly, so do 932 other people, and they've got tickets to his talk on Sunday.
She clutched my arm. "You don't understand," she hissed. "I'd do anything. Couldn't I just - bring him drinks or something?" Her face suddenly clouded. Damn it all, she was after all a product of Cheltenham Ladies' College. Half to herself, she concluded, "Or would that be too servile?"
The literature festival director's lot is a happy one. When not having conversations like that, you become institutionalised for two weeks and normal life goes on hold. You spend solitary, monkish days writing introductions and interview questions and preparing for the vast, rumbling wheel of the programme schedule that will roll over your life and the lives of 300 authors and 100-odd helpers, caterers, organisers, drivers, backstage Johnnies and ticket-tearers; then the first day comes, you grab the vast metaphorical wheel with both hands and cling on, and you never stop moving for 10 days.
The concept of time remains (the days become filled with curtain-up deadlines and radio-interview deadlines and Sir-Michael-will-be-at-the- station-by... deadlines) but other concepts disappear: the idea of eating hot meals, for instance, or paying for drinks with cash, or having negative thoughts, or remembering that you once lived in a London house rather than a Cheltenham hotel...
The job is simple. Just a matter of finding amusing things for 300-odd talented writers to do. Ushering a multitude (42,000 this year, the largest ever seen en fete litteraire in the UK) into the presence of someone they've hitherto met only in private, in the act of reading their words.
Discovering an excuse, under the Millennium-Dome-sized umbrella term of "literary festival", for inviting a hundred non-bookish celebrities (dancers, cartoonists, chefs, wine buffs, drug-smugglers, ex-prime ministers, pop stars, scientists, lawyers and fashion plates) who are guilty of Literature By Association because they've got a book out this year - and seeing how they get on. It leads to some startling convergences.
In the Writers' Room last Saturday, amazed eyes watched as a collection of higher Bohemians hovered and flapped and mingled and swooned over each other.
At the centre was the Magwitchy figure of Ian Dury, in his mother's Gypsy- lace scarf, flanked by his hirsute minder Del and the model Marie Helvin; joined by Arthur Brown (the artist formerly known, in 1968, as The Crazy World of Arthur Brown); Molly and Sophie Parkin; Howard Marks, the nation's most lovable drug-smuggler; Christopher Logue, the century's finest translator of Homer; Jeff Nuttall, the jazz cornettist and author of Bomb Culture; Charles Shaar Murray, the motor-mouthed rock critic; Terry Pratchett, the Tolkien of Discworld... Five minutes' walk away, Sir Edward Heath was arriving at the Everyman Theatre, to be interviewed about his autobiography.
Earlier, rumours had flown around that he and Howard Marks would be sharing a green room. What on earth would they say to each other? ("So, er, Howard, how did you enjoy prison life?" "Fancy a joint, Sir Edward?") But, sadly, the knight's minders kept them apart.
For every punter who wondered about the presence of media stars and TV celebrities at a book thrash, there were a dozen who marvelled at the audiences attending the serious stuff.
What brought 250 souls to a lecture on Virgil by Peter Levi? Or brought 200 to hear Pushkin's newest biographer, Elaine Feinstein, reveal that the duellist who killed Russia's greatest poet was having a gay affair with the Dutch ambassador?
Or got 300 enraptured souls to listen as a bearded Oxford professor called Michael Nicholson described how Alexander Solzhenitsyn had turned up, as a walk-on part, in no fewer than four published spy thrillers?
(It's easy to explain the Solzhenitsyn audience - GCHQ is just around the corner, and the town is crawling with retired spooks.)
Anything English, classic and female gets audiences of 500-plus. Last year it was Clare Tomalin on her new life of Jane Austen; this year Kathryn Hughes's irresistible lecture on "George Eliot in Love".
The people who attend are by no means all English graduates, or blue- rinsed valetudinarians; what they come for, pilgrims on the path to the Authorhood Grail, is to find out things: to "get" Pushkin, or Virgil or Shakespeare, in a single hour, to hear a biography-length life reduced to handy proportions, to learn how poems or songs or novels get written, to have someone explain a hexameter, or the "structure" of a wine, or the process of combing the NKVD archives (as Antony Beevor did) under the hostile eye of a former KGB colonel while researching for Stalingrad.
They come in homage to the imagination of the person they've been reading, and stick around for the learning-curve.
Inevitably, the biggest audiences were for people for whom books are incidental - television and stage and music and parliamentary stars, who've committed their thoughts to print during a break from their "ordinary" lives. Thus Jeremy Paxman, Judi Dench, Chris Patten, Ranulph Fiennes, John Simpson, Richard E Grant and General Sir Michael Rose walked off with the top attendance prizes.
But something happens to such people when they experience the creative process of making a book. Their books are generally far from thrown-together volumes. They're mostly well written confessions or apologiae pro vitis suis, or stylishly mendacious autobiographies.
And the act of writing them invariably plunges the new author into an unexpected ferment of self-appraisal that defines her, or him, in a new context. The act of writing democratises the media star/politico/tap dancer/professional hitman and turns him/her into a new voice in the Cheltenham Babel, one that they may never have heard in their heads before. A transforming voice.
Take Ian Dury, meeting whom was the highlight of my own festival experience. On Radio 4's Today programme last Saturday, I'd endured the scorn of Auberon Waugh, who pooh-poohed the festival's celebration of "the literature of rock'n' roll", saying bluntly that we were simply sucking up to the young (Mr Dury is 56; his core fans, myself included, are in their mid- forties) and concluded by quoting Keats's "Ode to a Nightingale" as an example of the immortal Real Thing. I argued my corner with Waugh, then later asked Dury, on stage, about rock lyrics and poetry.
Nah, he said, they were completely different things. "I 'ate seein' my songs written down," he rasped, because, he said, it made him realise how far behind true poetry they fell.
Whereupon he lifted his vast, grizzle-haired bonce to the hot lights and, with closed eyes, recited the beginning of Keats's "Ode to Autumn", word-perfect.
A shiver crept up the audience's spine. Mr Dury, from being the Cockney- roughneck-music-hall-Gypsy-showman as advertised, stood revealed as a thinker, a modest, well read poetry-loving cove who agreed with Auberon Waugh.
That's what festivals do: they treat the literati like rock stars; and rock stars (and ballerinas and pasta chefs and wine connoisseurs and bus drivers and Sir Edward Heath) as if they have a contribution to the world of letters that is worth listening to.