I guess if you are using public loo, you would be taking bottle of water in with you to wash it anyway, so i'd just pour it over my hands too, wipe them then wash properly in sink.
I've not got really heavy periods, but on forst few days, its fairly heavy. I've not been out, but have been using it at home and not had anyprobs as the cup contains all the fluid. and not much at all on outside. I suppose that because the cup catches it before it can get to the part of your fanjo that you reach into..
although, having said that, it seems that i have to reach 'in' alot further than most to retrieve mine. It should be just sitting at the opening with the tail there to pull it out with. SO, i'd say its not covered in blood...
sorry i've waffled a bit.