Without know more (specifics) about your current setup it is hard to say just where the distortion or the hissing is coming from.
However, let me guess.
Distortion - Typical of overdriving or having too hot a signal. Unless you have a device somewhere between your bass and the the soundcard, I would guess your soundcard is getting too much signal. This is probably either due to a natually too hot signal from your bass, or your soundcard is trying to amplify the input too much.
Hissing - Could be naturally noisy pickus (single coils), or an unsheilded control cavity, or poorly shielded cable, or your soundcard is trying to work too hard to make somethign of the input signal (this often goes hand-in-hand with the Distortion thing above).
Typically cheap soundcards typically have very crappy pre-amps. They are fine for gaming-headset microphones, but not much else. If you go into Windows, you might stumble across the "+20db boost" thing for you microphone input. Turn this off. Further, try turning the input volume on the soundcard down in windows. THe less internal amplification you can do on the soundcard the better.
My advice is to see if you have, or can beg-borrow-steal, a Direct-In box. There are many. Many amps now have them built in. Sansamp BDDI is a good one for bass. Radial, Behringer, Ampeg, they all make them. Amoung other things, a DI box is designed to plug an instrument into it, and do some internal amplification and impedence matching, and output the signal, usually with an XLR microphone cable, into a mixer (or in your case a soundcard). An XLR->1/8" jack dongle would be what you want. This should get you a nice clean, hiss-free signal into your computer. The added bonus of having a DI box and XLR cable is you could also run your bass directly into a PA system at a gig. Not at all an unusual situation.
As a point of reference, I paid $23 for 25' of mic cable, and $7 for an XLR->1/8" dongle. I already had a "balanced line out" on my amp, so that was all that was needed to feed my soundcard.
