Stunned by the outcome, she decided to ditch the show she was preparing to take to the Edinburgh Fringe last year and – almost overnight – write a new one about Brexit.
Because You Demanded It was the result - which received rave reviews and sold out its entire run - and now she is touring an expanded and updated version.
"It was a huge moment in politics," says the Gloucester-born comic of the EU vote, "and it would have felt like a real failure on my part not to talk about it. I was gutted, but I needed to make sense of it. Lots of people I know voted Leave...."
But although she herself is a fervent Remainer, Bridget doesn't want to preach to the converted – she is playing dates in several towns that voted firmly to Leave - and wants Leave voters to come along too. "More than any other show I've done," she says, "this one has been the most divisive, in terms of audience reaction."
She is avowedly on the left of politics, but says: "I don't know what right and left means any more, and Brexit has changed everything, the way we talk about politics, the way it's reported.
"I might find myself agreeing on the EU with somebody whose views on everything else I hate, then I'll read an article or see someone 'from the left' who I've always agreed with, that"s pro-Leave, and I think, 'How can you possibly think that?' Nothing is clear-cut any more. And even my core audience – lefty, feminist, Guardian-reading – is split, and that's a reflection of broader society."
But if you think a show about Brexit may be a bit heavy-going, fear not. Bridget is an entertaining host who leavens the passionate discourse with much faux outrage, and the show is full of playful mockery.
The show has expanded since its Edinburgh outing. "So much more has happened since the vote, including the growth of the "alt-right" and Donald Trump's election, and obviously I needed to update it. I also talk more about Nigel Farage than I did in Edinburgh," the comic says drily.
Is there a message in the show? "No, not really, not intentionally, anyway," she responds. "I just write about what I'm interested in and passionate about. I do enjoy the challenge of trying to talk about serious or important things in a funny way, though.
"I'm very interested in that process. It's like a puzzle you have to work out. So there isn't a message as such, but I did want the show to be a reminder of who did what and why during the campaign. Anyway, if people agree with me, then great, but equally it's important to engage with differing views. I want the audience to leave the show laughing and upbeat."
The blurb for the show, she reminds me, is: "If you didn't want to leave the EU, or you did, but now don"t, then this is absolutely the show for you.
"If you did want to leave the EU you will still find it funny, but for different reasons, as you witness the liberal female comedian"s exasperated and despairing meltdown."
She uses a clever gardening metaphor to tackle some of the big issues, such as the nature of Britishness and immigration, centring on the fuchsia that her mother, an Irish immigrant, lovingly tended in the home where Bridget grew up. Fuchsias, for the non-gardeners among you, are non-native plants but thrive in British soil...
I ask how she came up with that theme. "I never thought I would have a garden of my own," Bridget says, referring to the home she shares in north London with her husband and their two young children. "I genuinely love it and find it really therapeutic; it's a great way to switch off.
"When I was planting my roses it struck me that I will not see my garden mature, and that set me thinking about the futility of creating and nurturing things.
"But you can't not fall in love because you might have your heart broken, or not have children because you're terrified of what could happen to them.
"I thought I could incorporate those feelings into the show, and it strikes me that people always get that bit because we can all relate to loss and fear."
The show she had planned to do last year – which she had started previewing before the EU vote, and which may see life in 2018 - was inspired by American surgeon Atul Gawande's book Being Mortal, and is her reflection on death, dying and the possibility of an afterlife.
More light comedy, I say, and Bridget laughs. "I just thought there may be a show in all of that – in something we're all facing but we don't really talk about," she says. "I thought I might be able to make it funny. But then the Brexit vote came and death sort of became irrelevant."
Bridget Christie: 'Because You Demanded It' is at Brighton Dome on 4 March. Visit brightondome.org or call 01273 709709.