New Bioshock is in Development.
After the release of Bioshock Infinite back in 2013, the new Bioshock title has finally been confirmed to be in development by Cloud Chamber Studios, a newly established team at 2K Games which is made up of several developers involved in the making of the original BioShock and both of its sequels.
There is no real confirmation for the story setting of this new Bioshock title, but the President of 2K, David Ismailer, promised the game would continue in the series's tradition of "powerful narrative and iconic, first-person shooter gameplay." The next release will be in development for the next couple of years suggesting that the development process will be following in the steps of our next generation consoles and PC hardware releases.
Cloud Chamber Studio is the same studio previously codenamed 2K Parkside and is headed up by Kelley Gilmore, whose previous experience includes decades of work on the Sid Meier's Civilization and XCOM series at Firaxis Games. There was a further in depth interview with Gilmore by gamesradar about all things Cloud Chamber and Bioshock.
There are high hopes that at the Game Awards 2019 there might be a trailer teaser release for the new upcoming title, but this will remain to be seen. The good news is that for any fan of the original game series, a new title being confirmed to be in the works, is a great start already!