So I want to walk my way through an audio track and audition it 4 bars at a time. 
I set the quantize to 1 measure and select the 1st 4 measures in the time ruler.  I press shift+spacebar which loops the time range selection (first 4 measures).  Cool.
Now I want to advance the 4 measure time range selection to the next 4 bars (ie 5 - 8).
 
Is there a keyboard shortcut for doing that?  How about going backwards?
 
Thanks!

Hi. I would assume / suggest that you just change your range on the timeline. Others may know better.
All the best.

There's no keyboard shortcut per se for "jump selected region forward or backward." However, if you hover the cursor over the horizontal line in the yellow loop bracket,the cursor turns into a double left/right arrow and you can move the loop bracket left or right. If snap is set to a measure, it's pretty easy to "land" on the next group of measures.

If the "loop" part wasn't involved you could put Markers at the desired sections. This (I believe) allows you to navigate by markers (I think there is a keybinding or setting to Tab by markers... this would make the timeline jump directly to those markers).
 
Then to encorporate the looping aspect you can do what Craig says (by moving your entire "looped" point range select) with Snap enabled. I think you have to grab the bottom line of the yellow loop marker range select thingie.
 
Since you can Snap by Markers (IIRC) this, in theory (if Loop ranges obey snap settings as Craig points out) would snap the loop region to the next marker which a simple drag move.
 
Since I've never done most of that stuff (I have my own ways of doing things) I can't say for sure if it all works like that so check the manual on all the things I mentioned or maybe the other guys can help you refine the workflow.
 
Also... what is it exactly you are trying to do? Is this so you can record one section at a time multiple times then move on to the next section and do it again? If so there is a specific loop/punch record option that you can use to probably make it even more automatic. Again something I never use (because I prefer taking a couple seconds to gather my grey matter before doing another take and I have my R + Track + Spacebar (and when needed Ctrl + Z) system so engrained I can do it with my eyes closed.
 
Cheers.