Kevjmyers said:
C Ionian, D Dorian etc. over the C Maj. chord. However that second scenario you mentioned just opened up a whole new can of worms! Ugh!
OK. Keep in mind that this is just my (possibly idiosyncratic) way of looking at it, not gospel. For the first scenario (C ionian, D dorian, etc), the big answer is: it depends. IMO there are some situations where it's just a waste of time to think, now I'm playing C ionian over a C, now I'm playing D dorian over the C. You're still working with just the same set of 7 pitches, so it's a lot easier to think of yourself as playing within C ionian, but just emphasizing different tones out of the 7 available. No point making things more complicated than they have to be.
Now, suppose that you have not one chord but a progression in the key of C. C-Dm-Em-Dm-C-C-C-C, one beat per letter. Now, you could think of that as going from C ionian to D dorian to E phrygian to D dorian to C ionian, but why bother, when the chords are going by so fast? Since we're in C, and this progression is a diatonic one within C, might as well just stay mentally in C ionian and just think of yourself as emphasizing different tones out of the 7 available.
OK, suppose the chords go by more slowly--say, 4 measures of C, 4 of Dm, 4 of Em, 4 of Dm, 4 of C. Here, the sound of each chord has more time to "set," as it were. It's staying around long enough to feel like a kind of harmonic center for a few bars. In that setting, you *might* elect to think modally--4 measures of C ionian, 4 measures of D dorian, etc. The possible advantage of this kind of approach, especially perhaps for a rock bass player, is that it could help remind you that the "1" of the mode is your root, the note that you might want to lean on a lot. But again, you don't have to think this way. You could, once again, think of yourself as being in C all the time, and just emphasizing specific tones within the 7 basic options offered by C, to achieve specific harmonic effects with specific chords.
[Note: when I talk about thinking of yourself as being in C all the time, I don't mean that just wandering around in the C scale will work. Selection of notes matters. I'm referring to something similar to what Chris elsewhere has called parent tonality.]
There's a lot more to this, but let me pause for the moment. BTW, Chris is a practiced pedagogue and has posted a lot of good theoretical material here. You'd be well advised to look up some of his stuff, and Pacman's, and a number of others.
As for the second scenario, one point I'd make is that, as has been said elsewhere, the modes are tonalities in and of themselves. They're not *primarily* derivatives of the major scale, though practically speaking they can be derived that way. I've long argued that a lot of rock and pop, as well as folk, is essentially modal. Think of the million forgettable songs you've heard that go something like E A D A. Typically, the E is the tonal center, but you've got the D naturals in there, which are not in the key of E major. I would say that you would tend to play that song in E mixolydian for the most part.
There's a lot more to this, but hey, I've gotta catch a train. I'm sure others will weigh in with sage advice. Good luck.