Interesting that these words get confused. I've never heard of "canton" being used as a verb. However, "cantonment" was frequently used in the British army in the eighteenth and nineteenth centuries, usually as somewhere that an army would stay for some time, for instance when they were on picket on a border or during a longer lull in the fighting or during the winter. George Washington referred to the Continental army being in cantonments for the winter after what, Valley Forge? It was about the same time that the newly-fledged American government first learned that price ceilings on the staples necessary to feed an army don't work, a lesson they've had to relearn every generation since!
The term "bivouac", on the other hand was used to refer to a makeshift encampment created in a hurry when the army was on the move. This is the source of its modern usage in hiking/tramping and mountaineering. When you're climbing and intend to be out overnight and are unlikely to be able to pitch a tent, you take a large double-skinned goretex bag with you, called a bivvy bag. It usually has ropes attached to it which you can secure to screws or pitons set into ice or rock to secure yourself to the mountain. You generally get into your sleeping bag in a semi-seated or reclining position on a ledge and stuff yourself inside the bivvy bag as best you can. It's temporary and usually done in a hurry, hence the term "bivvy (bivouac) bag". It's also usually damnably uncomfortable, but that's another story!
