If you are planning to play through The Bioshock Collection, be aware that the save system has limited space to store your progress. The bundle only reserves a set amount of storage. This allocation is global as well, meaning that if you use it all in Bioshock, you will have no room left when you move on to Bioshock 2.
One user on the PS4 subreddit noted the consequences for not conserving your save allocation.
“I completed B1 and started B2. When I proceed to next level after half hour, AUTOSAVE couldn’t be done, even manual SAVE couldn’t be done because it said that save memory is full. So basically I lost my progress there.”
He is lucky he wasn't several hours in like another user was when discovering the bug.
It’s hard to believe that when 2K Games released The Collection in 2016, it intentionally limited the amount of space reserved for saves so much. This issue has been known about for quite some time now, and yet it still has not been patched.
The workaround is to delete most of your saves from Bioshock other than one or two of your endgame files before starting Bioshock 2 or Infinite. In a day of near-limitless drive capacity for saving progress data, it’s somewhat inexcusable that the games should be hobbled this way.
That said, the Bioshock Collection is a great way to enjoy the fully remastered series and all of the DLC on the PS4 (or PC/XB1), especially for the low, low price of zero dollars. All three games were initially released on previous generation hardware. They look and run even better on current platforms. Just be aware of this limitation and take precautionary measures before starting the next game in the series.