As a bass player, I am typically trying to either play something unexpected/less than intuitive, or really awesome. Only when I am asked to fulfill a role in a band with a traditional approach to the bass part do I consistently end up relying on standard sorts of lines or the expected notes (there are definitely times where it sounds better to just chug on the root of a chord and not come up with something fancy). One way I accomplish this is via inversions.
First off, I will address your notation. The way you wrote the chords in the question essentially spells out what the bass part should be. For instance, if you gave me a lead sheet with these chord symbols, I would play the notes specified below the slash. This is not always the case though. Sometimes when a chord chart is written for a specific instrument, as opposed to a generic one for everyone in the band, the symbols are written as you have indicated. For instance, you may find a guitar chord chart that shows D/F#, which would describe the voicing of the chord on that instrument, but then listen to the recording of the song and find that there is a D in the bass. In such a case, the guitar chart is accurate for the guitar player but not the band; if you were writing a chart for the band and wanted the bass to play the D, then you would just call it D, not D/F#.
I have a few different approaches to inversions. One of the more solid approaches I use is to use a linear thought process, ie, ascending or descending lines that move by step/smaller intervals. For an example: G, D, C could be G, D/A, C. This creates a smooth ascending line and removes the larger interval of G to D as bass notes. This also creates a much different sound for the D, which can make a standard I, V, IV progression sound a bit more unique than the expected roots. Another example for the same progression: G, D/F#, C/E. This creates a nice step-wise descending line.
One thing I find with inversions, specific to major chords, is that the 3rd in the bass tends to be more dissonant/less stable sounding and there are definitely reasons, such as the minor 6 interval being more dissonant (minor 6 from third to root). Additionally, minor chords in first inversion (3 in the bass) often sound like major 6 chords, especially minor 7 chords. As such, some Jazz theorists contend that there is no such thing as a minor 7 chord in first inversion, that it is actually just a major 6 chord. For instance, A-7= ACEG, C6= CEGA; same notes just a difference in bass note. This would mean that it would often make more sense when placing the 3 in the bass of a minor chord to actually reanalyze and call it a major 6 chord. This thought process holds a little less weight without the 7 but I still think it sounds more like a 6 chord than a minor in first inversion.
Some inversions will have stronger desires for resolution. For instance, placing the 7 of a dominant chord in the bass will make the bass note want to move to the 3 of the following chord (assuming the resolution is a standard V-I progression, if not, it may desire to move elsewhere). So for a G7-C, G7/F would want to resolve to C/E, which follows standard voice leading concepts. Another example, G7/B would want to resolve to a C in root position, as the B is the leading tone and has a tendency to resolve up to the tonic.
Some inversion possibilities are harder to accomplish in most settings. It is not too often that you will find a major 7 chord with the 7 in the bass. This is due to the 7 being a half-step below the root, causing a b9 interval, which is very dissonant. Jazz voicing theory suggests that if you have a b9 in a non-dominant (dominant including diminished chords or other dominant substitutions) you are actually changing the function of the chord, eg, if the root of a maj7 chord appears above the 7, they are suggesting that this would not properly fulfill the role of the maj7 and would instead have a different function, ie, requiring resolution within the chord or to another chord instead of existing on its own as a stable chord. Most often if you do find a maj7 with 7 in the bass, it will be followed by a chord with the same root but a dominant chord with 7 in the bass. For instance, G, Gmaj7/F#, G7/F, and would most often be followed by C/E with the 7 resolving down by step to the 3 of the chord of resolution. You will also notice that in this example the inversions create a descending line, like I often employee as described above.
Another approach I use is to imply other standard bass motions. For instance, in a progression containing C, A-, I may do C/E, A-. This implies a V-I resolution (E being the fifth of A). This is further strengthened by the relative dissonance of the first inversion major chord, which will desire resolution more than root position or second inversion. Another example, A-7, C could be A-7/G, C, employing the same V-I implication. Similarly, B-, G could be B-/F#, G, which employees the desire of the leading tone (F#) to resolve to the G.
Similarly, sometimes I will use inversions to create tension on an otherwise stable chord entirely for the purpose of dissonance. This can be good for prolonging a phrase, ie, preventing the feeling of a full resolution until the next phrase. This also works when the chord progression is shorter than the phrase and repeated beneath it, suppressing the resolution until the phrase is complete. For instance, a standard ||: VI/II/V/I :|| in C: A-, D-, G7, C over two phrases A-, D-, G7, C/E, A-, D-, G7, C. This keeps the C in the middle of the phrase from feeling resolved, which makes the C at the end sound even more resolved by comparison. This example also happens to utilize the example shown above with C/E moving to A-, the E to A bass notes imply a V-I resolution. This could also be complimented by putting the 7 in the bass on the G7 preceding the C/E, giving the 7 resolving to 3 in the following chord as mentioned above.
I have also found that diminished chords tend to sound rather nice with the 5 in the bass. I'm not really sure if this has to do with how the guitar players in my indie rock/prog rock band voice these chords, or if this is relatively common. With diminished 7 chords being symmetrical, this could also call for renaming the chord.
I also like to use inversions just to create a different feel for a chord or set of chords. In one of the songs my pop rock band wrote I use the 5 in the bass for the two chords in verse: C, Dadd4, becomes C/G, Dadd4/A. This changes the feeling of the two chords but ultimately still conveys what our singer/songwriter intended. Typically putting the 5 in the bass is the most consonant sounding inversion, so it is easiest to employee, while giving a new feel to the chord. I actually use the above mentioned inversion in the chorus section as well (the G, D/A, C example). On the whole, this makes some relatively standard progressions sound less standard. I also find that once you start using inversions throughout a song, the difference between the root position and inverted chords tends to matter/stand out less. It seems that the ear gets used to the somewhat less stable sounding chords and it becomes an acceptable texture for the piece as a whole.
I do still often find myself trying to invert a chord and being entirely unsatisfied with its sound, even though the same application worked elsewhere, so experimenting with different inversions will make you much better at finding what sounds good and when you are just trying too hard. Like I said initially, some chords just sound better with a big thick root in the bass.
For the one chord progression you have provided above, it will be all about how things flow for you. I would first try all of the chords in root position and see which in particular feel like they could use something different or a smoother motion. I might try something like the below (I'm not sure how this would sound since I am not at a keyboard to try it out, if only my ears were so good...):
Am, Dm7b5/C, Am7b5/Eb, Em7b5, Em/B, Am, G7, Dm7b5/Ab, Am... (assuming it repeats)
This gives you ascending, linear motion to the Em7b5, then jumps down to the B and proceeds to descend by step until the last chord, which steps back up and is enharmonically equivalent to the leading tone of A (G#), which leads nicely back the Am at the top of the progression (again, assuming it repeats). This same use of an enharmonic leading tone takes place on the Am7b5/Eb resolving to Em7b5, where Eb is enharmonically equivalent to E's leading tone, D#.
Now that I have written possibly the longest answer in the history of SE (though I doubt it), I would suggest you work out the different permutations to find the best way to voice these chords, which may just all be in root position. Remember, trying to add/change ideas based on theory can be great but it by no means will consistently give you a "better" sound/song; it is all about choosing what is right to accomplish a sound you want. I think that this use of theory can be incredibly helpful in creating unique sounding progressions but always let your ear be the guide in the end, not your mind just thinking, "that is so theoretically cool it has to be the best choice!"