From what I can guess, I don't believe the JB62/LH/3TS is canon. The animators needed SOMETHING to work with, and with the greatest amount of detail put into that 3D model in the intro, I'd have to say that's what the studio had hanging around and decided on that.
Kinda confusing, I know. I guess you'll have to decide on your OWN, what bass Mio uses. Make it YOUR canon. After all, no one else will ever be able to tell you otherwise, unless Kyo-ani shapes up and starts being more consistent with their instrument portrayals.
I mean, just read what Justice posted. One of those sites is claiming Mio's bass is an actual '62 vintage. Like she'd have the money for THAT.

No way she'd simply window-shop at Mugi's store if she were that loaded.
Personally, I would go for the JB62-US. Less Japanese, perhaps, but not a single thing about the bass can be contradicted.