There are two parts; the transmitter and the receiver. The transmitter connects to your bass. The receiver connects to the amp. The receiver can run off a battery, but since it is stationary on the amp, it doesn't hurt to run it off a power supply.
I'm going to assume the transmitter runs on a 9V
How long does the battery last? After I get a new bass im going to take the $200 or so from christmas and buy an X2 wireless