I've owned many crappy basses. But I've cycled through so many, I don't keep any of my GOOD basses, let alone my bad ones. Currently I have a '07 Nash JB-63 and a German Warwick FNA.
I can think of 4 basses I thought were "bad" by some measure:
My first bass, black Yamaha. Late 80's, early 90's entry level, used, was like $100. It did the job, but wasn't great. Only one pickup was working and it took me 2 years to figure that out.
Traded it in towards bass #2, Dean Edge 4. The good, beautiful, easy to play, very light. Bad, $0 resale value, tone wasn't great.
Bad bass #3 was a Peavey Foundation Fretless I got. This thing had been abused in a previous life. It was poorly stripped of a black finish, and had a heavy and poorly applied poly clear coat on top. Also they didn't remove the pickups when doing the poly, so they were basically epoxied to the body itself. A bit of a disaster.
Bad bass #4, wasn't really too bad. I got a very cheap knock off Ash P body. I finished it myself, put a Mighty Mite neck on, Fender Original '62 and pickguard. What made it bad was the body dimensions weren't exact, so the pickguard had to be forced into position to be around the neck pocket, the pickups and still put the pots in the top route. That and the fairly cheap hardware made a good sounding great playing bad bass.