2K has announced that a new Bioshock is indeed in the works. But after Bioshock Infinite, the team at Irrational Games disbanded- with a smaller team under Bioshock creator Ken Levine forming Ghost Story Games and are working on another project. And the team that did Bioshock 2, 2K Marin, is no more. So 2K made a new studio.
Called Cloud Chamber, the studio has a presence at San Francisco- with ex-Firaxis Kelley Gilmore as the Global Studio Head. Cloud Chamber also has a studio at Montreal, headed by former Zynga GM Ken Schachter. Cloud Chamber is wholly owned by 2K.
The next Bioshock is in development “for the next several years”, so it’s early days still. So expect the new entry to be for the next generation of consoles.
Ars Technica confirmed that Ken Levine and his studio are not involved with the next Bioshock. However, a few former staffers that worked on past entries are in Cloud Chamber, including Hoagy de la Plante (as creative director), Scott Sinclair (art director), and Jonathan Pelling (design director).