Doug,
Like you, I'm a keyboard player. When I'm playing, there are two principles that I keep in mind...
1. If a bass line is being played by a friend on bass guitar or by Band In A Box, there is no need for me to worry about playing any bass at all. In fact, if I did play bass, it is more than likely that I will create bass-note conflicts with the bass line being played. Such low frequency interactions are uncomfortable for the listener.
- For example: while C and E played together in the middle octave range (say above 200 Hz) sound fine, when they are played together as low-end bass, it doesn't usually work. Dissonant intervals in the bass are even worse!
2. If there is no bass-line provided, then my playing provides that.
With the above in mind, while I don't have to jump down to specific bass notes all the time, it is necessary to keep bass movement in mind. The principle I always use is...
If the bass note is a dissonace (any interval other than those below)...
- perfect octave
- perfect 5th
- major or minor 3rd or 6th
...then that bass note would need to resolve by a step of either a tone or a semitone (usually by a step downwards).
With this in mind, if I played your example of FGBD for a G7 chord in the middle octave of the piano, my next chord would have the lowest note E or Eb (this could be EGC, EbGC, EAC, EGB, etc.).