The tanks on an RV are holding tanks and not a septic system. There is very little "breaking down" via bacteria and enzymes that occurs in between dumpings. If waste broke down that fast, household septic tanks would never have to be pumped.
As far as getting a little bleach water in your black tank, I would not worry about it. According to Oregon State University (and many others) "Because it is unstable, when used for disinfection, diluted bleach should be prepared fresh daily". Add to this the fact that using the black tank adds water which dilutes the bleach even further means the odds it will be able to kill anything becomes pretty much zero quickly.
http://oregonstate.edu/dept/larc/sites/default/files/pdf/chlorine-fact-sheet.pdf
