Most basses have a stereo jack and use the mono plug to short from the ring to the sleeve to connect the battery.
If you're really creative, you could wire a stereo cable to supply the power to the bass (tip = signal+, ring = +9V, sleeve = signal & 9V grounds). You would need to create a box that has the stereo jack to the bass cable, a 9V power input jack, and a mono out jack to your amp. You'll also need to short across the 9v connector inside your bass.
You'll probably want to add supply filtering inside your box as well, since most wall warts are not filtered and will cause your bass to hum.
All in all, it's quite a bit of hassle, which is why I've never actually done it. Getting good 9V batteries and changing them regularly is a lot easier and cheaper.