I've listened to most of the tunes mentioned in this thread and mostly they bore me and I can't get through the whole thing. Sometimes the performance is flawed, sometimes I think, "this is really good, I SHOULD be liking this" but I don't. It's tough to compete with saxophones, pianos, violins, guitars, singers, etc, not to mention entire bands and orchestras. The only one I could get through was the string bass player going over the top with Purple Haze.
At its best the bass guitar has a sort of sad, mournful beauty that no other instrument can get, sort of like a basset hound. For bass guitar solo covers I'd go with Jeff Berlin. He has everything. Lots of classical guitar influence. I don't know why he isn't more famous than he is. Star Spangled Banner Tears In Heaven
Here's an amateur who plays beautifully. Darren Frate doing Kate Bush. Who would even think of this, much less pull it off. This, I can listen to over and over. And Dream OF Sheep