O.K., I'll try to tackle this in a way that makes sense:
1 Lord
6 I
5 will
1 lift
2 mine
3 eyes
4 to
3 the
#1 hi-
2 ills,
Key C
C /
A /
G /
C /
D /
E /
F /
E /
C# /
D /
Now, because I've heard the song before, I know what chords are used on each bass note. I also know the melody of the song. So, I fill in the chords using inversions that keep the melody notes on top:
C / E-G-C
A / E-A-C
G / F-G-B-D
C / E-G-C
D / B-D-F
E / C-E-G
F / C-F-A
E / C-E-G
C# / A#-C#-E-G
D / A-D-F
For me, it's about having a good ear for the music. I know a major chord when I hear it. I know a dom7 #5/#9 chord when I hear it, etc. That's because I've practiced them over and over and over again. The bass notes for me are all about the structure of the song. If you break down enough contemporary (or any other genre) songs, u will start to see the same chords being played for certain bass notes. So, over my years of playing, I made a list of all of those chords. For example, if I see a 2, chances are it's gonna be one of about 6 chords: major, minor, minor 7th, half-dim7, maj9, dom9. Example of chord options for 2 in the key of C:
D / D-F#-A *Dmaj or just plain D
D / D-F-A *Dmin or Dm or d
D / D-F-A-C *Dmin7 or Dm7
D / D-F-Ab-C *D half-dim7 or Dm7(b5)
D / F-A-C-E *Dmaj9 or DM9
D / F#-A-C-E *Ddom9 or D9
Which one do you use? Depends on where the music is going. If it goes to 3 or 4, I would go with the Dmin, Dmin7, or Dmaj7. If it goes to 5, I would use the Dmaj, Dm7(b5), or D9. Knowing all of these chord options eliminates me having to write out all the harmony notes. I just pick a chord and keep it moving.
My whole fascination with the number system came from my theory classes in school. One of the first lessons I learned about was the figured bass. You outline the bass notes, then build chords on top of it. We also learned about the musical zip code, 3-6-2-5-1. This is the organization of chords that have the strongest flow. 1 is ur home and the idea of a song or progression is to build ur chords so they end up back home. Home is usually where the ear is happiest. After we got good with that, then we learned about melody and how to build chords underneath the melody. The melody process was longer and more complicated in my opinion.
Those numbers that aren't in the scale, like the C# in the above song, can be traced back to a number in the scale. In this case, it traces back to 6. How do I know that? Because the next number is a 2. If u look at the musical zip code (3-6-2-5-1), 6 leads to 2. So, in actuality, it's an inverted 6. In classical theory, we would call those chords V of Vs, or secondary dominant chords.
I think I'll stop right there and let that marinate. The number system is basically theory with your ears coming along for the ride to make sure it sound good. If you've never taken theory or learned about it, the number system won't do you any good.
You see SOJ, the same way you've learned your harmony method, I've done what with the number system. So, trying to learn a new method seems like a waste of time cuz you're more or less stuck with the method that works for you. Your method works just as well as the number system. In order to use either one, u gotta 1st believe in the system. That's where testimonials and demonstrations help. Then u gotta stick with it long enough to have it work for you.