While MIDI information is indeed 1's and 0's, it's not audio. It's performance data - I played this note, this hard, held it for this long, and applied this pitch modification (bend, vibrato) - which then has to be used to trigger audio, typically from a synth. It can't translate a whole lot of the nuance of your playing, however, since it won't know the difference between a slapped note and a fingered note of equal volume, for example. You also typically have to deal with latency, or the delay in time between when you sound the note and when the system can recognize and translate the performance data. Since that latency is frequency dependent, you'll get more latency with bass than guitar, and more latency the lower the note you're playing.
If you want to output digital audio, you would still need some sort of transducer (like a magnetic or piezo pickup) which would translate the physical energy of the string into electrical energy, and then an A/D converter to convert the (analog) electrical signal into 1's and 0's. You would then have to plug that into something that accepts a digital output.
What are you trying to accomplish? If you want to plug directly into a computer, I know there are systems for guitars that output the signal digitally on a USB cable, and you might be able to find something like that for bass, but even then, I'm not sure what good that does for you over an external converter other than convenience. If you're trying to plug into something else, it might be easier to do it another way.
