So, I can tell you what I know from a bassist's PoV.

What I posted was the 12 bar blues chord progression in Roman Numeral notation. What it tells you is that if you start in the key of C, the other bars are 4 and 5 notes up from C. In addition, since the notation is in uppercase, the chords / arpeggios you can play in that bar are major not minor. So, if a bassist is playing a walking bass line for 12 bar blues, they'll probably start those bars with C, F and G. But, since they're C major, F major and G major, the bassist can play major arpeggios in that key in those bars and it will sound good.

For other kinds of blues progressions, if you know Radiohead's "Creep", you can see that as being an 8 bar blues with the following progression:

| 1 | 2 | 3 | 4 | |

|

|

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| | I | III | IV | iv | | I | vi | ii | V7 |

So if the root is C, the 2nd bar is E major, third bar is F major, 4th bar is F minor, and so on. Because the 3rd and 4th bars are both rooted at F the bassist can just play an F there and it sounds good (which is what I think Radiohead's bassist does), but if the bassist chooses to play more notes in an apeggio, they have to play notes from the F-minor scale in that 4th bar or it doesn't match.

As for why those various chord progressions happen to work, that I don't know. I don't know if anybody does. But, I do know there's some math / physics behind it. A perfect fifth is one of the most pleasant sounding intervals, and those notes are at a frequency ratio of 2:3. The only better sounding thing is an octave at 1:2. And, the inverse of a perfect fifth is a perfect fourth. So, songs being made from 4ths, 5ths and octaves makes sense.