The Xbox 360 controller cannot, by itself, send Bluetooth. You have to go through a computer of some kind (such as a Raspberry Pi) if you want to turn it into Bluetooth. It might be easier to make it go through a plain serial adapter (with longer range) such as an Xbee Pro.
Another option is to get something like a Spektrum DX5 with receiver, which is a RC controller with a few channels.
You have between three and five channels you need to control:
1) Left and right, or forward/turn, for the wheels. A motor controller with built-in mixing would be easiest for this. An onboard microcontroller (Arduino, Arbotix, Axon, Teensy, or similar) plus some plain motor controllers is an alternative.
2) Gun activation. This is turning on and off a power switch, basically. Maybe something like this: http://onyxrobots.com/2014/02/14/coming-soon-onyx-fire-ii-control-board/
That board can receive serial commands, or RC-style PWM commands, or simple logic-level signals to activate a switch that can drive an airsoft gun. (In fact, that's what I use it for!)
3) Gun aim. You may want pitch (up/down,) and you may want heading (left/right,) each of which needs a servo with reasonable capacity, plus some mechanics to make it pivot correctly. Or just tie the gun to the chassis and fire straight ahead.
The easiest solution is probably:
1) Get the Wild Thumper
2) Get something like this controller: https://www.sparkfun.com/products/12075
3) Get a Spektrum DX5 with receiver
4) Get the Onyx Fire board
5) Drive it all with a 2S LiPo battery
6) Mount the gun on the Wild Thumper directly, and aim by steering (simplest)
Disclaimer: I made the Onyx Fire board, and I haven't actually listed them for sale yet. But any day now!