Regarding the "Bebop" scale:

There are actually more bebop scales than the Dom7th that Barry references here that use the same concept of adding a passing tone to create an eight note scale where you can get all of the strong chord tones to land on the downbeat.

While you're practicing them, remember that you can start on the Root, 3rd, 5th or 7th and ascend or descend and still get the sound of chord tones on the strong beat. There is the tendency to always start from the root, but remember the other options.

I was taught to acces the various modes of the melodicand harmonic minors by starting the MM or HM scale from a note located in relation to the root of the dominant chord I was playing over (altered scale is MM played 1/2 step above the root of the dominant 7 chord). I think I understand that the Phrygian Dominant is a harmonic minor played a fourth above the root of the dominant chord (C HM over G7#5). Is that correct?

I also was taught to play major, melodic minor and harmonic minor in all 7 positions. So I can also see G phrygian dominant as the fifth fingering of a harmonic minor scale (which starts on G) laying over the G7#5 chord. This way it is easier for me to see and play the G, the G# (b2) and the F(b7).

When I play that mode starting on G, rather than C, Ithink my lines sounds more like a Phrygian type mode. But my brain tells me it shouldn't really make a difference because all the notes are under my fingers under either formulation.

Am I imagining this or am I missing something?

You're totally on track.The way you hear pitches is in relation to the chord sound in your ear. If you were hearing a G7b13 chord, the phrygian dominant ascending would sound very phrygian. I still would work on making sure I could play that mode from any Dom7b13 chord shape you know.

Thanks again,
Barry