I see what you're saying, but in fact, in normal usage, neither instrument is generally considered that. Both are typically considered instruments of the string family, in which sound is produced by strings being set into motion (this includes both bowed and plucked strings).
The basic Western classification is strings, wind instruments (including not only woodwinds but also brass), and percussion. Of course this system is far from perfect. Where to put keyboards, for example, is an issue, since they have strings but make use of hammers to strike those strings and set them in motion. There are other omissions as well. (How about those hammered dulcimers?)
But this is basically what we're working with, and I think it's fair to say that it's something like a common understanding. If you have a choice between strings, winds, percussion, and (maybe) keyboards, you pretty much have to put the bass guitar in strings, not percussion.
There are other classification systems as well, of course. All of them, like this one, somewhat arbitrary.
I've been perusing this thread and waiting for someone to say this.
Richard is absolutely correct. I have only ever seen the arguement of wheather an instrument is stringed vs. percussion with regard to the piano. Everyone knows that this instrument has strings that vibrate, but only do so because they are struck. On the other hand, this arguement was never made for the harpsichord since it's strings are plucked even though the harpsichord is very similar to the piano.
Instruments which are classified as percussion (not the bass) can also generate pitch, such as the xylophone, the typmani, and infact standard drum heads can be tuned to an actual pitch (if you have enough toms you can actually play a tune on them).
As Richard has demonstrated, the bass is a stringed instrument based on the traditional definition. However, there have been bassists (i.e. Cliff Burton) who are known for literally striking the strings and slamming them against the pickups. In the effort of trying to keep an open mind, I would say that this is one instance where the bass could be considered a percussion instrument, but not in its traditional role.
