Chord tones! You gotta love 'em!
Well, the answer is probably rhythmic. I bet that that g-Bb-c bass line puts that c on the "1" of the bar (or the 3) very likely. So the other two notes are setting up that big "here is the root note!!!" on a what we humans feel as a strong beat. And yes, the inversions are just starting on the next notes in the chord and going up in order - starting on 3rd is first inversion, starting on the 5th is second, the 7th is third.
A general rule of thumb would be: If you put the chord tones themselves on downbeats (so on the 1,2,3,4 not on the upbeats) then they outline the chord the strongest, and within the downbeats themselves, the strongest beats in a measure of 4/4 are beats 1 and 3. So if you put the strongest chord tones, (the root, and then the thirds and 7ths and then the 5th) on those extra special downbeats of 1 and 3 you will really hammer home the type of chord you are playing.
Now, of course there are a million styles of music and specific songs which don't do this exact thing for a specific reason or effect and play off the beat on purpose, but if you are doing blues or anything rock-y or jazzy this is a good general rule.
The best book by far for this concept is called "Forward Motion" by Hal Galper, and he basically invented/discovered this concept and explains it in a very easy to understand way. He shows how this concept of how we perceive certain beats as stronger than others is universal, it has nothing to do with jazz or blues, it goes back to Bach's time and he shows examples where Bach uses it.
I wrote an article about this beat placement and chord tones recently also. Download it and check it out, and it is easy to hear it work for yourself. There is a link to Hal Galper's explanation of this concept as well. I have no affiliation with Mr. Galper or anything, just a big fan of his work.
http://bassoridiculoso.blogspot.com/...ord-tones.html
The examples use pentatonics, but the same exact concept applies to arpeggios, scales, whatever.
This rhythmic principle is also the reason behind the Bebop scales (major minor and dominant), those scales fiddle with some extra notes to make the harmonically strong chord tones line up with the rhythmically strong downbeats in a measure so that you can open up a double whammy of tonality reenforcing whoop arse on that chord.