Amaj9 A9 | Bm7(b5)/F Fdim | Gdim* Bbm/A A9 | Bm7(b5)/F Fdim |
(*I would write the C# in this chord as a Db)
I think that "my aural skills said so" is a perfectly valid answer to the question "why is it OK to play this note here?" But if you're looking for some theoretical justification of why the A works under those chords, I would say it is functioning as a pedal point.
That question is impossible to answer as presented, because you have provided a single measure without any context for what else is happening in the song and in the harmony. Given the way you stated the question, the best answer is, "it depends" -- it depends on the desired sound and what else is going on in the arrangement in this measure. In each measure here, you have a Cmin7 followed by an Emin11. Playing an Ab in the bass under the Cmin7 will make it an Abmaj9. Each of the four choices presented for the Emin11 will have a different sound. Which of those sounds do you want? That's what the bass should play.
With that said, if I were looking solely at the way the chord in the top staff is voiced and selecting a bass note without any other context, my first choice would be an E.
Now what exactly is the point of this exercise?
Having a degree in music, this is the exact answer I came up with as well. It's all about how the chord functions and stacks up.