Since my only option is a coin-op DIY wash, I find that it's easier and faster to just pay the $3.50 and only use the sprayer. The brushes are too coarse and frankly, I prefer to do the job myself.

Getting back to the orginal topic: Re-using dirty soapy water from a bucket is less effective and has a greater risk of damaging the clear-coat.
This is particularly true with a sponge, because grit will tend to accumulate in the pores of the sponge over time.