Many a time music is held up as awesome or pure crap based solely on the listening preferences of the folks making those judgments, but for the most part even things we hate aren't bad music. I don't particularly like insipid and repetitive pop for example, but I can at least recognize it as competently executed music I really really hate.
Bad music on the other hand is music that fails at being music. If you like bands that do nothing but scream over top a thrashing wall of noise that sounds indistinguishable from a series of explosions, then you're pretty much musically retarded and you have my pity. Other notable examples - bands where the lead singer is either incredibly tone-deaf or just pure malevolent evil incarnate for singing like somebody who is tone-deaf intentionally, music where two distinct and non-complimentary tunes are played at the same bloody time (modern 'classical' music loves doing that), music that has no tune at all, a horrific combination of everything I just mentioned, etc. Bad music isn't just music you don't like, it's music that actively punishes you for ever having the audacity to listen to it.
Thankfully most music you run into that you despise will just be annoying or stupid rather than unholy perversions of the medium of sound.