Ruby Wax. The name conjures up spiked hair, red-lipped pout and archly comic tongue. She was being funny in prime time when British television had little room for funny women.

Before she embraced the stereotype of gobby American, Wax was a serious actor, doing a stint in the 1970s with the Royal Shakespeare Company. But she is most famous for her TV work, which ranges from appearing in the comedy series Girls on Top to script-editing Absolutely Fabulous.

When we speak she is on a coach, returning from a seminar – we'll come back to this – and doesn't want to annoy other passengers by talking loudly. This seems at odds with her huge personality and the talky, insightful interviews she did on her TV show Ruby Wax Meets . . . in the 1990s.

But what most people didn’t know then was that as Wax held court with Imelda Marcos and Salman Rushdie, she was struggling with her mental health. “I had three- to five-year gaps between depressive episodes,” Wax says, “but I was lucky, because I didn’t have a regular nine-to-five job, so when I was sick I was able to stay home.”

In a Ted talk in October 2012 called What's S o F unny A bout M ental I llness? Wax explained that she assumed that if she had a breakdown it would be because of a "Kafkaesque, existential revelation". Instead it engulfed her on the day of her daughter's school sports day. She went to bed for a month and woke up in an institution. "I never told anyone. I only 'came out' about it because Comic Relief put me on a charity poster, so I became a bit of a pin-up girl for mental health."

A few years ago Wax wrote a solo stand-up show, Losing It, which played at Edinburgh Festival Fringe and many other venues, but those crowds were not the first to see it. "I performed it in institutions, and they were a pretty responsive audience. After two years of performing in front of people who could possibly turn on you, there was nothing frightening about showing it to the public."

That it took such a long time for things to get so bad is surprising, given the entertainer’s childhood. Her parents fled Austria after the German Anschluss, settling in Illinois. Her mother had obsessive-compulsive disorder and was constantly critical of her only child.

Wax says she was first diagnosed with depression when she was just 10. "I told my parents that I felt sick, so they sent me for blood tests, because everyone thought it was a physical thing, but no one really knew what it was until much later. And depression is a physical disease, but it's often hard to pinpoint."

Her early interest in the brain was a factor in her choosing psychology as her college major at the University of California, Berkeley, and in her television work Wax frequently returned to it.

Even though she was presenting high-profile shows, she says her health meant it was time to go. Some reports suggest she was let go. Did this have anything to do with the BBC’s apparent belief that woman presenters have a finite shelf life?

“I wouldn’t have gone on anyway,” she says. “I did the TV stuff for 25 years, and it was time to move on. As people we’re meant to reinvent ourselves, so that’s what I did. Some things are appropriate at a younger age that are not when you’re older.”

Still, Wax presented Ruby's Room , an online series for the BBC in which she interviewed people about mental-health issues: bipolar disorder, agoraphobia, gender dysphoria and depression among them. "For me, when I got depressed I didn't know what it is. It just feels like you have the 'flu."

Wax says that her new book, Sane New World: Taming the Mind, and her Irish appearances this weekend are not about her mental health. Her stand-up show is about neuroscience, our mindset and how we can learn to fix ourselves in what can feel like a frantic age.

Wax is qualified to do this, because in the intervening years she has been studying. A lot. She has a psychotherapy certificate and last year graduated from Oxford University with a master’s degree in cognitive therapy.

The course has also formed the basis for her Sane New World show. Wax believes that our lives have become too cluttered and our brains painfully overloaded. "The new show is about all of our plights, about how busy we are, about the constant barrage of bad news, and how we're born fearful and have to work really hard to be positive."

One of Wax’s favourite aspects of touring is talking to audiences afterwards. “People come to the show and learn stuff; they get excited. That’s the payback for me. I love piecing people together like a Rubik’s cube . . . Actually, everybody is giving me bad looks. So I’d better get off the phone.”

And with that Ruby Wax – therapist, comedian, red-lipstick wearer – is gone.

Ruby Wax is at An Grianán, in Letterkenny, today and at Theatre at the Mill, in Newtownabbey, tomorrow