She recalled: "Years ago I was on OKCupid. I had an hour and a half to finally meet this guy for a drink - I'd been talking to him for months.
"He arrived and looked nothing like his pictures but I persevered. I realised I was doing all the talking. I hate that, and he said, 'I'm just imagining being back at your apartment naked.'
"I looked at him, took $20 out from my purse and said, 'I'm going to go now. Have a nice day.'"
Laverne is proud to be an inspiration to other transgender people.
Asked what she's most proud of, she said "That through my work I've inspired others to live more authentically as themselves and to transition. A lot of people tell me they've been inspired by my story."
The 'Doubt' actress also admitted she has learned how to move around unrecognised - but doesn't want to reveal her disguise as her cover will be blown.
She said: "I have an incognito way of moving through the world, and everybody makes fun of me for it. But I'm not going to tell you what it is, otherwise I won't be incognito."