Most clear disposable deli cups that would be used for water bowls, are (in 2011) polypropylene (PP), which is one of the most recyclable, and recycled plastics currently in use.
So long as the water bowls are consciously recycled, I'd say this is less wasteful on a large scale than running several batches in a dishwasher.
Use plastic cups (just recycle them)!
With a little digging, I'm certain you would be able to find polylactic acid (PLA) AKA corn plastic, deli cups, which are biodegradable. Natureworks is a large producer of PLA. Keep in mind, that some research has shown that during breakdown of PLA, methane gas is released.