HIV is a blood borne disease, transmitted via blood. If we are talking blood transmission of HIV, then transmission to the child or anyone can be done only if the blood was fresh and the child had an open wound receptive to that blood. Fresh air will kill the HIV virus in a short time. I have never heard that HIV, even in fresh blood, being transmitted via water. HIV is easily killed outside the body and cannot live on surfaces once it dried up. If the problem is HIV, it was probably dead already if the blood is dried up. Hep C can be transmitted even if the blood is dried up, but again the child would have to have an open wound herself.
Im not an expert either, but I would say transmission of anything would be pretty near impossible!
I'm no expert, but.......unless you have some sort of illness (and I'm thinking HIV or something) that could be transferred to your grand-daughter through your blood I don't see any need to worry. Blood by itself is not harmful to anyone. Are you worried about transmitting something specific?