What did they evolve from – guitars, or bass fiddles?
Both. I have no really authoritative answer to your question, but since this is CS and not GQ, I can offer an opinion, right?
Upright acoustic basses are of the violin family of 4-string instruments. Electric basses (I believe) have the four strings tuned (even though an octave lower) to the bottom four guitar strings – E A D G – a perfect fourth apart. I confess to not being sure if the bass viol or double bass is tuned in fourths or fifths, but I wager somebody else closer to the facts will add those details shortly.
Take it away, Bass Man…
WAG of a former bass player, but I believe they developed from bass fiddles. Same EADG tuning, and serve same function in groups. (Of course, they are the same tuning as the bottom 4 strings of a guitar.) But the bass fiddle was used in folk, blues, and bluegrass, as well as early rock and much present rockabilly and such.
I believe the guitar developed from the lute.
I’m sure someone who knows will step in can clarify the development of the guitar and violin families.
(The violin is tuned GDAE, a tuning shared by the lute-family mando.)
Also, some folk play basses with 5 or more strings, with various tuning.
The normal EADG tuning is identical to the double bass.
The bass guitar was invented as an easily transportable (and playable) alternative to the bass fiddle. The first popular bass guitar was the Fender Precision bass,introduced in 1951, the design of which was based on Fender’s electric guitar design e.g. the Telecaster. So musically it was certainly based of the bass fiddle but designwise was based on the electric guitar.
In fact the italian lute and the spanish guitar developed independently from the arabian oud. The violin developed from the rebec, which itself was probably developed from the arabian rabab, which was in turn probably developed from the oud. so all these things are fairly close cousins. Also, the bass fiddle is not considered to be of the same immediate family as the violin. The bass fiddle was developed from the bass viol, whereas the violin coexisted with the viol family. The viol family had frets and was tuned in fourths. So the genealogy of these things is really quite intricate if you go back far enough.
The double bass originally had 3 strings (File:Domenico Dragonetti.JPG - Wikipedia). Today 4 and 5 strings are both common, and a lot of classical artists will have extensions put on as well all in an effort to extend the range of the instrument (Bill Bentgen - 5 String Basses ). I’m not sure about the development of the tuning of the double bass, but some players tune in fifths (http://www.talkbass.com/forum/archive/index.php/t-45144.html).
Btw, this is my first post! :eek:
Six-string basses are also pretty common, though four remains the standard.
Welcome aboard, guppy!
Thanks! 
I’m so honored that you came out of the shadows for my question, guppy!
Interesting links – thanks to you and everyone else who answered.
Well done F n’ B! Really not much to add, except to say that Fender’s P-Bass was amazing in that it was invented pretty much fresh - unlike, say, electric guitars, which had precedent for both being played in a similar position, for amplifying old-style hollow-body versions and for other attempts at amplifying them (e.g., resonator guitars), the P-Bass was the first attempt at taking a standard, upright 4-string bass, and flipping it on its side and electrifying it using a solidbody construction. And the sucker worked perfectly - to this day that basic design is the main one in use. Really quite remarkable. And the P-Bass was the first popularly made double-cutaway shape - soon after immortalized in the design of the Stratocaster in '54…