Check out the bass in
this link.
That may not be Alderete playing, as this is Paul Gilbert live. but as I recall the bass was very close to what you'll hear on this.
Pay attention to the bass after each of the arpeggiated sections on guitar, and check out that sick unison line that the guitar and bass play in the middle after the drums drop out.
I'm not a shred guy personally, but I remember getting one of those little tear-out 45's in G****r Player years ago, and I couldn't help but be impressed by the chops.
Yeah, I'd say he qualifies as a shredder.