When dumping water the dirty water is not as much as an issue as the debris in it is what creates odor and attracts animals. So strain the water with a fine steel strainer and then throw away the debris in the garbage.
When running rivers and tent camping We set up a three bucket system, that is a leave no trace ethic. One five gallon bucket for "spuge," to first rinse the debris into, then a soap pan and a rinse pan. If we are using river or stream water I do a third pan with bleach water. All three are collapsible, the bucket, and "river" sinks are square roll up. I got them from Campmor or Sportsmen's Warehouse. I have had them for about 10 years so they last. When done with then I clean then from clean to dirty, dump the spuge through the strainer, pour the soap water in the spuge clean and dump through the strainer, pour the rinse/clorax water in the soap pan, rinse it, then in the spuge and all is clean!