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Double Bass Playing the I7 as an approach note from I to IV?

Yeah. Actually, this sounds like what I was asking about, except that you're indicating using the ♭7 (F in key of G) on the third and fourth beats on the way to the IV instead of just the fourth beat. So you're suggesting that pedaling the ♭7 like this sort of legitimizes it? And you hear this as becoming more common in bluegrass today?
I think what he was saying was something like this chord progression:

G / / / | G / F / | C...

Chords, not bass notes
 
I think what he was saying was something like this chord progression:

G / / / | G / F / | C...

Chords, not bass notes

So, does this supposedly only work on guitar and/or piano with chords, but not as individual notes on the bass? If the guitar and/or piano are playing an F chord on the way from G to C, then it's okay for the bass to play an F, but not if they're playing a G7 chord on the way from G to C? I don't see why that would be.

Would pedaling the F on bass for the 3rd and 4th beats of the measure on the way from the G chord to the C chord somehow legitimize ("realize"?) the use of the F compared to just playing it once on the 4th beat of the measure?

It even seems to me that there are many times when it sounds okay, or even good, for the bass to be the only one playing a particular harmony note that stands out—particularly when it creates some tension that anticipates the next chord change.
 
So, does this supposedly only work on guitar and/or piano with chords, but not as individual notes on the bass? If the guitar and/or piano are playing an F chord on the way from G to C, then it's okay for the bass to play an F, but not if they're playing a G7 chord on the way from G to C? I don't see why that would be.

Would pedaling the F on bass for the 3rd and 4th beats of the measure on the way from the G chord to the C chord somehow legitimize ("realize"?) the use of the F compared to just playing it once on the 4th beat of the measure?

It even seems to me that there are many times when it sounds okay, or even good, for the bass to be the only one playing a particular harmony note that stands out—particularly when it creates some tension that anticipates the next chord change.
What you were doing as said in the original post was that you were using
G / / / | G7 / / / | C...
or something to that effect. You played it as
Chords: G / / / | G7 / / / | C...
Bass: G / / / | F / / / | C...

This has a few problems:
  1. First of all, the seventh of a chord is generally (and I mean very generally) a tendency tone that wishes to resolve downwards by step. At the very least, it wants to resolve by step.
  2. When moving G-F that generally wants to keep moving by step, because the F, though a chord tone, is perceived more as a passing tone than harmonically functional.
  3. If the F were to function as a chord tone, then you have a G7 in third inversion, that is to say G7/F. This is a very tricky sound to work, and as a result is quite rare, which means that most ears aren't used to it, and can be considered dissonant when compunded by the previous list items. G7/F would never leap to resolve to the next chord, but instead would almost always resolve to a C/E.

G7-C is not the problem. The issue is simply the way you are choosing to express it. I think someone else mentioned a G-F-E-D-C walk to it, which would utilize the F-natural that defines the G7 (as opposed to a diatonic Maj7, which you would probably encounter very rarely in a bluegrass group). Your G-F-C move under G7-C isn't melodically functional (Yes I recognize that bass is not a melodic instrument generally, but in this instance it requires a certain ammount of melodic sensibility).

Bass motion of G-F-C is not a problem. The progression of G-F-C would make this a very sensible, if not the most sensible choice of notes. This progression is a problem only if your ears don't accomodate it; nobody here will tell you it's a good or bad progression.

However, the problem arose with how the bass motion worked within the chord progression. If you can express the G7 chord in a stylistically acceptable manner (e.g. don't enter a flurry of 64ths), then more power to you. The progression works. The question is one of execution, and you didn't execute it in a very "acceptable" manner. For example one thing that would be functional would be to (blasphemous as it is) arpeggiate. Most people wouldn't consider that idiomatic of bluegrass, but that would be one way that you could outline the chord. Of course, the ultimate thing you must answer to is the two flappy things on either side of your head; if it sounds good to you, then play it. For example one thing that would be functional would be to (blasphemous as it is) arpeggiate. Most people wouldn't consider that idiomatic of bluegrass, but that would be one way that you could outline the chord.
 
With other folks emphasizing the b7 as a leading note to the IV chord - either in the vocals or high note instrumentation like mando or banjo - the last thing the bass wants to do is jump on that note too.
As a melodic flourish, that 7th needs a home base to jump off of. You're home bass!
Try the 3rd (B) when they go from G to G7 it puts 'motion' in the mix while still defining the chord nicely. Your ears will teach your hands where to go!
 
With other folks emphasizing the b7 as a leading note to the IV chord - either in the vocals or high note instrumentation like mando or banjo - the last thing the bass wants to do is jump on that note too.
As a melodic flourish, that 7th needs a home base to jump off of. You're home bass!
Try the 3rd (B) when they go from G to G7 it puts 'motion' in the mix while still defining the chord nicely. Your ears will teach your hands where to go!

Well-put points by you, Roscoe. Sounds very logical, and others here have suggested the third, as well. I'll certainly give that a heavy-duty try.