Jesca Hoop certainly agrees. In the period prior to the release of her first album Kismet in 2007, the 34-year-old Californian singer-songwriter earned her keep looking after Kellesimone, Casey and Sullivan, the offspring of Waits and his wife, muse and co-writer Kathleen Brennan.

Unsurprisingly, Hoop describes the experience as “a dream come true. I was looking for a mentor at the time when I came to be with them. I moved from a small town in the country into working in the world of music, so it was a gift you’d never look in the mouth”.

Hoop is one of those American artists who arrives with an immaculately unorthodox back story and a pleasingly askew world view. She was raised in a Mormon family in the California countryside north of San Francisco, and brought up on folk, opera and classical music; the brash blare of MTV was strictly embargoed. Instead, her mother tutored her in a formal choral style, teaching her to “sing the way a ballerina would dance”, as Hoop puts it.

After damaging her vocal chords, however, she found her voice had changed. “I had to rest for about a year and afterwards I went back to the same choir and I was given a solo and couldn’t do it,” she says. “I was shocked that I couldn’t sing the same way.”

Hoop expresses love for Joni Mitchell and PJ Harvey, but it’s Kate Bush whom she credits with “teaching me how to sing like myself. My mum taught me how to sing but I rebelled from her and instead I listened to Kate Bush, and I learned I could do lots of other things with my voice. I had to become more like an actor in the way I used it”.

Not only did she reject the formalities of classical singing, she also rejected the Mormon faith. In her twenties she left California to work for a children’s rehabilitation project in Arizona, and eventually wound her way to Los Angeles and hence to the Waits homestead in her home county of Sonoma. She gave Waits a demo which found its way to influential Los Angeles radio station KCRW, and when her first album was released her boss conjured up a typically poetic endorsement. “Jesca Hoop’s music is like a four-sided coin,” he wrote. “She’s an old soul, like a black pearl, a good witch or red moon. Her music is like going swimming in a lake at night.”

Hoop giggles with delight. “It’s so beautiful, isn’t it? It’s the best thing that anyone’s written about me because it’s done the most good.” Indeed, with the world hardly lacking quirky female singer-songwriters, Hoop is well aware of the extent to which Waits’s seal of approval opened doors. “That’s why he gave me a quote – to help it make it through to the billboards. And it has, but I didn’t know it would be quite some time before I lived down the nanny bit.”

Even without the helpful nudge from Waits, Hoop would stand out. With her oddly spelt name – “little things help, don’t they?” – and propensity for Davy Crockett-style headgear, she’s hard to miss, but she also has the talent to back it up. Her second album, Hunting My Dress, is a work of real depth and beauty. Hoop shares Waits’s ability to make a variety of primitive musical forms come alive in the present.

She can change vocal stylings – and accents – in a manner reminiscent of Kate Bush on The Dreaming, and also shares Bush’s inquisitiveness and her ability to access and incorporate sources far beyond the confines of pop culture.

“If I draw from pop music I digest it to the point where it’s no longer visible,” she agrees. “I don’t use my contemporaries in terms of how I sing. There’s been something happening in the past five years where women are sounding the same and I don’t think I play any part in that.”

Before we get too carried away with Hoop’s other-worldliness, it’s worth noting that last year she relocated to Chorlton in Manchester.

Although it was love, not music, that dictated the move, she has already tapped into the local talent pool. On Murder of Birds on the new album she sings with Elbow’s Guy Garvey, another fan. “It’s a new chapter,” she says. “I’ve moved to a new country, gathering new players, and I’m starting to develop more.”

Chorlton will never be confused with Brigadoon, but it’s clear that life in the Lancashire suburbs hasn’t dented her heightened sense of romance. “The people I love the most, I imagine them cooking food, or bathing, or walking in the woods,” she says dreamily. She may have picked up some pointers from the master, but Hoop is clearly a natural.

Hunting My Dress is out now on Last Laugh. Jesca Hoop plays Nice’n’Sleazy, Glasgow, tonight.