On Tuesday, Nov. 4, during Week 8 of Dancing with the Stars Season 34, the ballroom transformed for “Rock & Roll Hall of Fame Night,” and competitor Dylan Efron delivered a standout Jive performance.

As the city unwinds after long workdays, Mumbai’s dance floors are coming alive again, pulsing with old-school jive and new-age joy. Held on weeknights, twice or thrice a month at different venues, ...