I've tried so many bass guitars and most sound the same if not alike, even the ones that cost $200 in comparison with pricier bass guitars.
I do find the Ashbory bass having a distinct tone. Is it the fretlessness of it or the strings or the pickups that give bass guitars their tone?
Rickenbacker 4xxx series?
Höfner 500/1?
Gibson Ripper?
Guild Starfire?
Gibson Thunderbird?
Gold Tone Banjo Bass?
Fender Aero Jazz?
Wal?
Dobro Resonator Bass?
…and more.
There’s quite a few with a distinctive or signature sound. How are you defining “distinctive?”
As far as the Ashbory goes, it’s unique sound is due to the loose rubbery strings. You can get an improved version of that sound on a mote playable instrument with any uke bass or a Gold Tone Microbass.