If you really need to cheap out on it, you can remove the wireless chip from an existing RC car and take over the H bridge inputs, or even just tap into the antenna input pin and inject serialized commands.
Most low-end 27MHz toy RC sets use clones of a well known chipset called RealTek TX2/RX2, and there are Arduino libraries for it. It only takes binary on/off commands for forward/back/left/right/"turbo" at 1Hz or so, which is fun enough for most purposes.
I put a link above for this kit which is about $50. However, I believe you would also need an ESC for the motor, a suitable one would probably be less than $20.