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Yeah, it will work with your bass guitar. but I think $25 is kind of expensive. You can probably pick a cheaper one up at an electronic store near you. Ask for a 1/8" to 1/4" cable.
It looks like this.

55-914-6.jpg
 
make sure that it has two black rings, like shown in the above piccy, this means that the recording can be stereo. if there is only one black ring itl be mono...which is really annoying.
 
make sure that it has two black rings, like shown in the above piccy, this means that the recording can be stereo. if there is only one black ring itl be mono...which is really annoying.

unless he has a bass with active electronics as well as stereo wiring (basses of this nature are uncommon and expensive), it won't make a difference.

When you plug it into your computer, it'll only play though the left speaker, as this is the part of the lead the guitar contacts with. Click the 'i' button in the bottom left, and where it asks for input, select Channel 1 (Mono). Also check that the input has been set to Line In in GarageBand preferences.
 
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