How big are the three Bioshock games? Will they fit on a Switch cartridge, or will they pull a Capcom and only include one of them on the card, and the rest have to be downloaded?
All of them were released on the Xbox 360, so they were on dual-layered DVDs (~9 GB). The total file size comes in at under 32 GB, so all games can be put on a card. With compression it could be feasible to ship all three games on a 16 GB card, but considering that the collection will likely be sold for $60, not even a 32 GB card can be a legitimate cost problem.
The file sizes of the remastered PC versions of the Bioshock games are about 20 GB per game, but texture data for high resolutions beyond what Switch displays increase file sizes dramatically. So there's a lot of space that can be cut for a Switch release if the Switch versions are based on the PC versions, similar to how the Crash and Spyro trilogies have file sizes that are only about a quarter of the PS4 versions. But speaking of Spyro, the catch is that AAA third parties are garbage companies, so in Spyro's case they used an 8 GB card and forced the other half of the data to be a download because they cheaped out on using a 16 GB card. While that was Activision, Bioshock is a Take Two IP, so looking at their track record would be a better idea. Take Two is bottom of the barrel, so the chances to see all Bioshock games on one card are miniscule.