First of all, if it doesn't work with your PS2 emulator you need the drivers.
If it does work with your PS2 emulator but not Bully, change the control scheme to Joypad [I think it is] in the control menu.
EDIT: I am slightly confused.
You say it's a "usb stick PS2" but you also say it says "Xbox 360 Compatible"
So I presume it's a 360 controller, not a PS2 one.