On a recent Friday afternoon, Joan Osborne stood outside 116 Macdougal Street, looking for traces of Bob Dylan. “This used to be the Gaslight Cafe,” she said, referring to the coffeehouse where Mr. Dylan played in his early days in Greenwich Village. It’s now a cocktail bar downstairs from a cookie shop. “We could get a cookie,” Ms. Osborne said, shrugging.
She had started her Dylan tour at Cafe Wha?, where Mr. Dylan performed as a New York neophyte in 1961. Reading from an online guide, she circled down to a townhouse at 94 Macdougal, where Mr. Dylan once lived, that is, until he got into a fistfight with a neighbor who had been going through his trash. “If you’re trying to be incognito, this is the last place you would buy a house,” she said. “So I don’t know what that was all about.”
Ms. Osborne, best known for her 1995 single “One of Us,” has had Mr. Dylan on the brain. Through March 11, she is performing an all-Dylan cabaret set at Café Carlyle, which has lately hosted such eclectic talents as Debbie Harry and Isaac Mizrahi.
The show is a reprise of her Carlyle debut last year, which also had a Dylan theme. The Carlyle had invited her to perform after she saw her friend Buster
 Poindexter play there. “It’s kind of like being an actor doing Shakespeare,” she said of her Dylan dive. “There’s a deep well.”
Not that she’s the world’s biggest Dylan obsessive. Growing up in small-town Kentucky, she was turned off by his “more vicious songs” such as “Like a Rolling Stone,” she said. “It seemed like it was about some girl who had dumped him, and it was just unnecessarily nasty.”
She was more into the Spinners and Led Zeppelin. Around 1983, when she was 20, she moved to New York for film school (she idolized François Truffaut and Bob Fosse) but dropped out when she ran out of tuition money. Instead, she fell in love with the blues.
“There was something about the emotional nakedness of the music that really spoke to me,” she said, strolling up Macdougal.
She was supporting herself as a receptionist when a neighbor on East 21st Street asked her to go to an open mike at a nearby blues bar. The friend dared her to sing a song, and she performed Billie Holiday’s “God Bless the Child,” revealing a smoky, snarly voice. More open mikes followed, then proper gigs, many of them in Greenwich Village.
“I used to play once in a while at the Red Lion, down on Bleecker Street,” she said, before sitting down for a cappuccino at Caffe Reggio, another old Dylan haunt. “One night I sang backgrounds for Carole King.”
Ms. Osborne, 54, has the affect more of a placid social-studies teacher than of a ’90s girl rocker. After releasing her 1995 debut album, “Relish” (it included a cover of Mr. Dylan’s “Man in the Long Black Coat”), fame hit her fast. Its breakout single was “One of Us,” written by Eric Bazilian of the Hooters, which imagines God as a “slob like one of us” riding the bus home.
The song became a top-10 hit, and Ms. Osborne, who describes herself as a lapsed Roman Catholic “who also happens to be a fan of Jesus Christ,” was nominated for five Grammy Awards in 1996.
The instant fame, she recalled, “was both incredible and horrible.” She was grateful that her music had found a wide audience but “didn’t love the feeling of being under the microscope.” With her bluesy voice and defiant air, she became part of a wave of mid-’90s female singer-songwriters that included Fiona Apple, Alanis Morissette and Sheryl Crow.
Within that formidable group, Ms. Osborne was determined to stand out. When she shot the video for “One of Us,” a makeup artist brought in a fake nose ring. “I thought I looked very vanilla and wasn’t rock ’n’ roll enough, so I wore it,” she recalled. “When the video came out, I was like, ‘Oh, my God, I’m going to look like the biggest poser in the world if I don’t actually get a nose ring.’”
Having long traded in the nose ring for reading glasses, Ms. Osborne now lives in a brownstone in Brooklyn with her 12-year-old daughter and her partner of nine years, the pianist Keith Cotton.
She has become more politically engaged lately, marching in protests (she was at Battery Park chanting “No ban, no wall” a few weeks ago) and organizing a benefit for the Tennessee Immigrant and Refugee Rights Coalition. Her family back in Kentucky includes Trump supporters, but, she said, “I have not figured out a way to broach that subject and have any sort of happy outcome.”
The Carlyle act has become more political, too. Since last year, she has added some more pointed Dylan songs, including “Masters of War” (“I just want you to know / I can see through your masks”). While putting together the set list, she even got a recommendation from Patti Smith: “Dark Eyes,” from the 1985 album “Empire Burlesque.”
Ms. Osborne did get to sing with Mr. Dylan once: In 1998, they recorded a cover of “Chimes of Freedom” for the NBC mini-series “The ’60s.”
“He didn’t talk a whole bunch,” she said. “The few things he did say were very acerbic.” She had just returned from Ireland, and gave him a bottle of expensive whiskey. “I don’t know if you drink,” she told him, to which he responded, “Oh, I might drink that.”