Ahh, TB...
OP posts that he is playing a Fender Jazz and is looking for an instrument that is similar and has a good B string.
And, of course, based on the B string, players are chirping up that the answer is some 35" scale or multi scale bass. Umm, no. Look, nothing at all wrong with Modulus or whatever. They certainly do have good B strings and are every bit fine instruments in their own right. But, referring to the OP, they are laughably NOT like a Jazz Bass. Not.
It remains a good question. Fender has made the 5 string Jazz for a while now. They have ironed out some of the wrinkles. One answer is to go play a whole bunch of Fender Jazz 5's, and find one that happens to have a decent B string. They are out there. But, IME, that 1 7/8" nut just has never felt "Jazz Bass" to me, even if everything else is right.
Then you've got the MusicMan 5's. No, they aren't Jazz Basses. But, that 1 3/4" neck and very focused B string check off a lot of my "Jazz Bass" boxes. IF you can find a light one. Probably the nicest production 5 out there that I have gigged.
If you have a bit more budget, then a Sadowsky, Lull, or Coppolo will definitely scratch the Jazz Bass itch, especially if you can get one with the 1 3/4" nut. They may be out there; but I have never played one of those with a poor B string. There are also the Xotic and Fodera NY designs; check out Jamareo Artis' sound on the SNL rendition of Uptown Funk on YouTube. If that ain't happenin' I don't know what is.
A bit further afield, the Zon Sonus has some Jazz Bass derivative design elements. It's neck produces an impressive B string.
There is a lot of subtle stuff that goes into a good B. Both bridge saddle and nut witness points are important, especially the bridge. Just one aspect is that compensation for string diameter with the other strings at the bridge required the B saddle to be driven much closer to the tail piece hold, resulting in a more severe angle for the thick B string. That higher angle for thicker string causes relatively more permanent deformation in the hardened steel core of the string. The severity of the witness point, knife edge vs rounded, is a further factor. All of which have consequences for the elastic vibration quality of the string. This is one aspect that is mainly ignored when comparing different scale lengths, because these kinds of details are also variable. So, the comparison is generally convoluted with several things not being the same between the instruments. Anyhow, the higher end builders tend to work all of this out for the player. We just talk about it as though we know what's going on. Unless one builds the instrument and struggles through all the details, you don't.
But, it's fun to talk about it.
