Baseline (Widescreen) Solution & Issues
Native support for widescreen resolutions. There is a "Horizontal FOV Lock" selection that needs to be disabled in the game-options screen. The HUD and all two-dimensional elements have vertical stretching in 16:10 and 15:9 resolutions. This includes the pre-rendered plasmid screens and certain pre-rendered backgrounds.
Ultra/Super-Wide (21:9/32:9) Specific Solution & Issues
The game works fine with the resolution selecting it in the menu. You just need to adjust the FOV to your needs if the default one isn't good enough.
Eyefinity / Surround Specific Solution & Issues
Flawless Widescreen has a plugin which fixes most of the problems (Menu, FOV, HUD). Only thing which is a bit off is the mouse positioning on the HUD and menus but it's still functional.
Get Flawless Widescreen here: http://www.flawlesswidescreen.org/
------ Old method ------
Resolutions can be set by ingame options but fov however can not.
To change fov to whatever you want you will have to edit User.ini file in C:\Users\username\AppData\Roaming\Bioshock
Look for entry:
F11=
F12=
and replace it with
F11=SetFOV 150
F12=ResetFOV
Now when in game: F11 key wil set your fov to 150 and F12 will restore it to native value.
Hud will be streched and you will need to press F11 everytime a level changes - but other than that game looks great in eyefinity.
4k UHD Specific Solution & Issues
Bioshock Recorgnises 4K Res natively and even notifies if it's widescreen yes or no.