I had just sat down on the top deck of a number 38 London bus when I saw him looking at me. He was black and wore a fake-fur coat and orange leggings. There were glittering rings on his fingers, fake diamonds around his neck and bright red lipstick on his lips. In his large hands, a mauve purse. He looked like the kind of Andy Warhol drag-queen who wiggled on the wild side of life back in the 1970s.

He made strange chirping sounds and he batted his heavy eyelashes my way. I couldn’t tell if he was a touch crazy or just over-the-top camp. Then he smiled at me. Uh-oh, I thought. But I decided to be brave, so I gave him one of my big, anxious chimp smiles back. He then came over and plopped himself next to me.

‘Hi,’ he said, with a soft, low American purr. ‘My name is Melissa.’

Gulp. What do I do now? I could just stare out of the window until my stop arrived. But no, I told myself, I will not take the coward’s way out. As an open-minded liberal who celebrates diversity and pluralism, especially in sexuality and gender, I should take the chance to engage with my fellow traveller. After all, there’s a brave new world of trans-this and bi-that emerging and we uptight straight men must learn to deal with it. So I will stay calm. I will be cool. I will be convivial.

And then he opened his coat and showed me his tits. My first reaction? Oh! My! God! My second reaction? Help!

So much for liberal tolerance.

Look, I must make this clear. These were not man boobs. These were woman boobs. Big woman boobs, jutting out of a man. I’ve seen this sort of thing in films and documentaries and I have known cross-dressers and drag queens. But I’ve never had the up-close, in-your-face experience before.

Naturally, as a good liberal I will defend to the death any man’s right to bear women’s boobs, but I have to admit I found it freaky.

And then I realised: I was having my first encounter with a transgendered person. These days the transgendered are every-where in the media, in soaps, films, fiction and conversations But despite their cultural ubiquity, you rarely meet one. That’s not surprising considering that such people make up a tiny percentage of the UK population. One estimate puts the figure as low as 5,000.

Now back to those boobs. It was the way he flashed them, with his big ‘Ooh naughty me’ smile, that made me wonder: was he just having some fun with me? Here was his chance to make the guy in the suit sweat a little. And then I felt his leg move and snuggle up to mine. We were now joined at the knee.

No doubt he expected to have me dashing and screaming for the exit. But some modicum of pride inside me wanted to fight back. I felt like saying to him: Madam, I have news for you — this is one uptight straight guy who doesn’t scare so easily! After all, in the 1970s I lived for a short time in the gay district of San Francisco, where every form of sexual lifestyle known to man or beast coexisted. This was the pre-Aids era when gays were fearless, flamboyant, in-your-face and up-your-arse American ‘faggots’, as they called themselves; not your domesticated, bourgeois gays of today. You’re going to have to try a lot harder to freak out this heterosexual!

Then he put his hand on mine. OK, that did it. Off went my internal alarm: Mayday! Mayday! I was about to get up and get off the bus and walk the next three stops in the rain when I thought: it’s just a hand. Stay calm.

But what do you say to a black transgender stranger in such a situation without causing offence? ‘Excuse me, sir… err, I mean madam, can I please have my hand back?’ Would he think I was a racist? Or trans-phobic? Or maybe both?

I started to babble on about how white my hand was and what an interesting collection of rings he had. There followed a competition to see who would remove their hand last. I’m proud to say I won.

The funny thing is that earlier that evening I had been on a date with a woman I had never met before but had been fixed up with by an expensive dating agency. She spent the time talking to me about the horrors of her ex-husband and showing me pictures of her children, her home and her horse. It was dull.

My new friend spent the rest of journey showing me pictures of himself in various wigs and outfits and then pics of Angelina Jolie, Rihanna and Madonna while providing funny comments on each one. We discussed favourite films and singers. And he told me his mother never speaks to him: ‘But that’s OK, I have many nice friends.’ I had more in common with him than my earlier date.

Then he stood up and said, ‘It was a pleasure to have met you’, and off he went into the rainy night. I was sorry to see him go.

Cosmo Landesman was one of the founders of Modern Review and is the author of a memoir, Starstruck.