I used to have the same issue with prince of persia the sounds of
time, since I had an old ps2 gamepad with adapter I fixed all the
joypad compatibility issues.
I believe the issue here is that with the regular Bully SE files and Wine's own dinput8.dll the joypad support works, but as Bully SilentPatch (build 3) uses it's own dinput8.dll it's not working with a Wine bottle. Most likely because the abstraction layer needs to come from Wine and the DLL used in Silent Patch has no way of doing this as it expects to be running natively on a full Windows install. I tried setting up Bully SE in a Vista Wine wrapper just in case this miraculously fixed the issue, but of course it doesn't.
So the choices are run the game without silent patch and have gamepad support (I use a wired Xbox 360 controller) or run the game with the silent patch and not have gamepads at all. Or the way I was doing it before, which was use Parallels Desktop with a Windows 7 VM which then gives you SilentPatch, gamepad support, 60fps but is an incredibly inefficient and resource intensive way to do it. 😂
I think you can use some of this tips taken from protondb. I'll post
this one maybe can help you for the silent patch: Launcher:
Steam
Downloaded Silent Patch (build 3) and unzipped in game directory.
Not sure if it's necessary, but the game is reported to crash often
without it.
Game window minimizes after splash screen
Changing the resolution screws up the game window, needs a restart
Intro video doesn't play. Watch it on Youtube to get some context.
Try to find the equivalent of gta ginput for bully for better 360
controller, visit nexus.
As by default CrossOver uses an XP based Wine bottle it'll likely not crash inside that controlled environment. Intro video I'm not worried about; I've seen it a bunch of times anyway (been playing this since it came out years ago).
What's this about GTA Ginput? Now this is a new factoid I wasn't aware of.