How quickly can the body restore energy reserves mid-ride/post-bonk, and how do we optimise this?
I'm interested in how we can maximise restoring energy stores (mainly glycogen, but I'm deliberately being vague) either between closely spaced rides or on long rides.


On a ride

Here your ability to actually rebuild glycogen stores are compromised as your body is trying to fuel the activity not rebuild your stores.

Exercise actually alters your physiology, for example the blood flow to the gut is restricted. As such, severe or exhaustive exercise actually inhibits gastric emptying and interferes with gastrointestinal absorption. This makes it difficult to absorb food, why easily digestible  foods such as gels were invented. 

Your insulin response is also greatly reduced during exercise as your body is trying to keep your blood sugars elevated so it can create high energy molecules (e.g., ATP) through glycolysis which in-turn are used to power your muscle contractions.

As long as you continue to exercise your body will prioritize creating energy over rebuilding stores, so rebuilding or recovering from a bonk while riding will always be severely compromised. The short answer is on a ride DO NOT let your glycogen stores get depleted. The general rule of thumb is eat something easily digestible carbohydrates at least every 45 minutes. The idea is you want use ingested carbohydrates to elevate blood glucose levels, rather than relying on your glycogen stores, which can be depleted relatively quickly (e.g., within 2 hours)

In-between Rides

Here refueling within the first 4 hours post-ride can be critical:


  Finally, take advantage of the glycogen repletion window that facilitates muscle glycogen repletion in the 4 hours immediately following vigorous exercise. During this time, any carbohydrates you eat are converted into muscle glycogen at up to 3 times the normal rate. And this window of opportunity closes fairly quickly as some data suggests there is a 50% fall in this super charged repletion rate by 2 hours with a return to the normal repletion rate by 4 hours post exercise. (Ivy JL et al,J Appl Physiol 1988 Apr;64(4):1480-5).
  
  [...]
  
  After this initial 4 hours surge, muscle glycogen stores are replenished at a rate of approximately 5% per hour. And while it may require up to 48 hours for complete muscle glycogen replacement following a 2 hour ride, for all practical purposes glycogen stores are almost completely rebuilt in the first 24 hours post event.
  
  [...]
  
  
  The rate of glycogen repletion is highest in the first 2 hours and then begins to fall off.
  Is more better? Although the rate of CHO incorporation into muscle glycogen storage begins to fall at 2 hours, there is a maximum repletion rate in the range of 1.5 grams of CHO per kg body weight during the first 2 hours post exercise. Thus a strategy of taking all your CHO replacement in the first few hours is not going to work.
  
  
  http://www.cptips.com/recvry.htm


Summary

There are physical limitations to how fast we can rebuild stores. The optimal strategy is not to let your glycogen stores get depleted if you are planning on completing back-to-back endurance bouts.  

A lot of this comes down to strategies:


Nutrition, before, during and after;
Not digging too deep on earlier rides, or too early in the final ride (i.e., pacing);
Minimizing your effort where ever possible:


Skipping pulls in the group;
Never letting gaps form between you and your daft; and
Not running a pannier (these are essentially parachutes), instead try a frame bag or a larger saddle bag, as the latter has very little drag.