Why would anybody use "bloody" to describe how would they take their burgers or any other food?
That sense of bloody means undercooked, so much so that pink juice comes out of it when a fork is put in it. The pink juice isn't exactly blood, but the expression is an exaggeration.
An explanation for why some people say bloody to describe doneness could be an incorrect, literal translation from another language.
For example, "rare" is called saignant ("bloody") in French, and al sangue in Italian.