I've got a solution, but it'll involve buying another piece of hardware...
Basically, I use a Line 6 Toneport, which is a ridiculously good bit of kit. It goes in the USB, you plug your guitar in, change the tone on a computer program, you play. You can also do guitars by plugging a microphone in and pointing it at the amp. And you can do bass by plugging the bass into the Toneport and changing the tone of the bass then recording directly, no need for amps or anything. That way you get the direct bass signal, and no problems with frequency response.
Well, it's how I've recorded the bass for my band's first album, and it's sounding pretty sweet :D