is there such a thing as a bleeding tree
This is not entirely incorrect since there is such a thing as a peachtree borer, and cherry trees are the primary host plant, and one of the symptoms of infestation is gobs of gum leaking from the tree. However, peachtree borer is not the only thing that will result in a cherry tree experiencing bleeding gummy sap. If the gum is emerging from rather high up on the trunk, rather than from near the root crown (the favorite spot for peachtree borer infestations), the bleeding is not likely to be caused by peachtree borer.