Is there a description of and explanation for the order of washing hands (left-right vs right-left) before bread or on waking (and other times)?
The order is always first filling the natla and passing it from the right hand to the left (so the mida of chessed, which is denoted by the right side, overcomes din, which is denoted by the left side), and pouring first on the right hand. This is mentioned in the Shulchan Aruch (siman dalet, seif-katan yud and Mishna Berura there).
This is done because the right hand, and generally the right side, is considered more important, and it is the side which G-d himself "uses" symbolically in many biblical contexts ("yemin Hashem osa chayil", "hoshia lo yemino", etc.)
Kabbalah says that when you first wake up, there are spirits in your body that leave. Only a few stay, and they are in your hands. They also say that when you are washing, these spirits jump from hand to hand, so you have to "chase" them. This is the reason for alternating from hand to hand.
However, when washing for bread, you are only removing the Tumah from them, not spirits. So there is no reason to alternate back and forth.