Dropsy, as we all by now, is not really a disease, but symptoms of a disease. One might liken it to coma in the sense that the state of unconciousness is not a disease but occurs because something is affecting the brain.
Dropsy is a swelling that occurs in the fish's body that can cause eye swelling and body swelling, enough that the scales stick up like a pinecone. Anything that can cause 'edema' will appear as dropsy. Kidney blockage by infection or tumor or parasites can produce this appearance. As Wilder has noted, one can try and treat for infection but dropsy is usually fatal.
There isn't one specific bacteria that causes dropsy, but, the only treatment we have is to try with antibiotics (Maracyn II here in the US) and use a salt bath.
Coming down with a severe infection related to fish is extremely rare and when it does occur, is usually limited to skin infections and then again, mostly if the skin is broken. In humans, mycobacterium tuberculosis is the bacterium that can cause tuberculosis. Believe it or not, it is very hard to transmit and one needs prolonged contact over a long periods of time to do so. Fish can carry TB, but, if you don't have a cut on your hands and you wash after putting them in the aquarium, there shouldn't be a problem. Can it be transmitted tho'? Yes...to skin.
I don't recall any instances of dropsy being transmitted to humans.
SH