As far as I know, a DS4 should work fine through Steam. The joysticks are not used - is that possibly what you're running into? If it is, you can use Steam to remap the controls if you want joystick movement.
Here is a simple remap if you want to try it:
steam://controllerconfig/bloodborne%20psx%20demake/2816129592
But I'd recommend messing around with your controller configuration until you find something comfortable for you. The configuration I personally use is more complex than the one I shared - it automatically holds the walk button when I only slightly push the left joystick; right trigger activates a macro that opens the menu, scrolls to right-hand weapons, transforms the weapon, and closes the menu; when I hold left bumper to bring up the gun cross-hairs, it makes the right joystick control the camera instead of the left ("aim down sights" camera controls work with the d-pad by default so you can aim up and down, where the normal camera, controlled by the triggers by default, cannot be aimed up and down); that kind of thing. If that interests you or anyone reading this, let me know and I can make a shareable version of that.
I hope the lack of joystick functionality is all it turns out to be and you don't need to go digging for another solution! I wish you luck, good hunter!