I bandage of someone"s cut finger, it was bledding and I eat something with unwash hand. Is there any possibility disease? I was not sure wether my hand has blood or not..

Yes, . Yes, you could get sick from ingesting someone's blood.If there was no visible blood on your hand, then the chances can be relatively low. Hiv virus dies in the open air. However, it is always essential to wash your hands anytime you come in contact iwth body fluids to prevent the spread of infection, incuding your own body fluids.