We have reused Cidrs as well, We do double rinse system. We have one bucket of clean water and a second bucket of water with Nolvasan Disinfectant Solution diluted with water. We pull them from the cow, dunk and swoosh in the first bucket and then dunk and swoosh in the second bucket. Then we lay them on clean paper towels until they dry. Also we put clean water in the first bucket about ever 15 cows.
In my opinion reusing cidrs only makes sense if you have a lot of cows, If you reuse 150 cidrs then the price goes form $10 to $5, and you save $750.
P.S. If we pull a cidr and it's covered in manure we just throw it out, but about 95% of the time they come out fairly clean.