It's actually a tricky problem. Better tell us what soundcard you have and what size / how many plugs it has. If it's a typical consumer-grade soundcard (soundblaster etc.), then it probably has a 1/8" mono mic input and a 1/8" stereo line input.
The next question is: Is your bass active or passive? it matters...
First, forget about the soundcard mic input - it's not designed for instrument or line level, and it's probably a very poor quality preamp anyway.
On the other hand, if there's a 1/8" line input AND you have an active bass, you can get by with adapting mono 1/4" (from your bass) to stereo 1/8" (on the soundcard). I don't know of a single adapter that will do that alone. There might be one. Radio shack probably has a couple of adapters you can combine: e.g. 1/8" stereo to 1/8" dual mono, then connect a mono 1/4" to 1/8" adapter to that. Clunky but it'll work.
On the other hand, if you have a passive bass, there is no easy way to connect to a line-level soundcard input. You really don't want to plug directly into a line-level input; you'll lose a lot of level and treble and the sound will be dull and lifeless. This is the problem that DI boxes are designed to solve. Unfortunately DI boxes are normally designed to connect to mic preamp inputs on a mixing board. So you either need to track down a DI with line-level output (e.g. the sansamp XDI or BSDR, or the MXR M-80), and then still get the 1/4" to 1/8" adapters mentioned above, or get a regular DI *and* a mic preamp or small mixer.
BUT - hang on! Maybe your bass rig already includes a preamp, or maybe your bass head or combo amp already has a line level output - sometimes there is an effects send that can be used just fine for this purpose. If so, all you need is the 1/4" to 1/8" adapters and you can connect this line-level output from the bass amp directly to the soundcard. No DI or mic preamp needed even with a passive bass.