Welcome to Talkbass!!
You probably need to look into getting some adaptors that will turn the mono-jack from your friend's bass into either an RCA jack or a mono or stereo mini-jack. You should be able to find these at an electronics hobby store (Maplin, Radio Shack). Most TV's have some kind of audio input usually used for playing back video and audio from video cameras etc. It may be hidden out the way though. You can (as you say) hook it into the PC through the soundcard input usually using a mini-jack. Using the soundcard's mixer will allow you to mix the levels and possibly center the sound (if you're using a stereo mini-jack, the sound will only come through one channel, but the mixer ought to allow you to compensate for this and get a mono signal in the middle of the stereo field).
BUT You ought to be really careful on
ALL of these options not to blow the speakers of your TV/stereo/PC. Basses can put out quite a lot of signal. Most things you'll play through your TV/PC/Stereo have had the extremely low frequencies toned down (compressed) so that the overall "loudness" can be increased without the low frequencies ruining your speakers. SO please be really careful. It would suck enormously to blow the speakers on your TV...
You might be surprised how cheap a second hand small practice amp is, and this will give you enough volume for jam sessions, and still be really portable.
Better that, than forking out for a new TV/Stereo...
Have fun, but play safe...
