This is an interesting question. I’ve liked a good few basses, and even then, it can vary from one example to another of the same model—not always predictable!
But, let’s see if I can find the common features of the ones I own and have liked best:
Slim neck - I guess I mostly been in terms of the depth of the neck, because I’ve gotten along with the thin nut width of a Vox Sidewinder and the wider width of the Squier Classic Vibe 50s Precision bass. However, even if it’s thin, it can’t be much wider than the P. Nut width has a limit for me.
Lightweight - My two main basses (a Peavey Foundation and a Fernades 4001 clone) are pretty light—as are most of the ones I’ve really liked (Epi 60s T-bird, Gibson Ripper, Rick 4003, Gibson EB3). I think my ceiling for weight is 10 lbs. I’ve played some boat anchor Precisions before and didn’t like those much, so much as I think they’re awesome, I couldn’t play something like a 12 lb Peavey T40.
Tonal Variety - I love being able to tweak and transform the tone on the fly to get different sounds for different songs. This is one of the things I enjoy greatly about my Peavey. It’s also something that appeals to me about active basses I’m after like the Kawai FIIB or perhaps, in some distant future, an Alembic. (As an aside however, I don’t mind a bass having just one real tone if I like it a lot, but, as this is supposed to be ‘perfect’)
Looks That Catch My Eye - Very subjective of course, but just as important to me as all the above—hard to play it if you aren’t into looking at it! This is a bit harder to pin down though… as I feel like I like a lot of different body shapes. I’ve been told I like odd guitars. I dunno, I just know when I see it. Like how I was taken by the Peavey and the T-bird when I saw them in the store, or seeing musicians I admire playing the 4001, the Ripper, or an Alembic.
Beyond that, I can’t really think of any other criteria!
But, let’s see if I can find the common features of the ones I own and have liked best:
Slim neck - I guess I mostly been in terms of the depth of the neck, because I’ve gotten along with the thin nut width of a Vox Sidewinder and the wider width of the Squier Classic Vibe 50s Precision bass. However, even if it’s thin, it can’t be much wider than the P. Nut width has a limit for me.
Lightweight - My two main basses (a Peavey Foundation and a Fernades 4001 clone) are pretty light—as are most of the ones I’ve really liked (Epi 60s T-bird, Gibson Ripper, Rick 4003, Gibson EB3). I think my ceiling for weight is 10 lbs. I’ve played some boat anchor Precisions before and didn’t like those much, so much as I think they’re awesome, I couldn’t play something like a 12 lb Peavey T40.
Tonal Variety - I love being able to tweak and transform the tone on the fly to get different sounds for different songs. This is one of the things I enjoy greatly about my Peavey. It’s also something that appeals to me about active basses I’m after like the Kawai FIIB or perhaps, in some distant future, an Alembic. (As an aside however, I don’t mind a bass having just one real tone if I like it a lot, but, as this is supposed to be ‘perfect’)
Looks That Catch My Eye - Very subjective of course, but just as important to me as all the above—hard to play it if you aren’t into looking at it! This is a bit harder to pin down though… as I feel like I like a lot of different body shapes. I’ve been told I like odd guitars. I dunno, I just know when I see it. Like how I was taken by the Peavey and the T-bird when I saw them in the store, or seeing musicians I admire playing the 4001, the Ripper, or an Alembic.
Beyond that, I can’t really think of any other criteria!