Bloodborne pathogens per description are all those viruses and bacteria found on human fluids , now by them self they can be dangerous and contagious. Correct handling of any materials and surfaces that has been in contact with this pathogens is the difference to prevent greater contagion risk. 

Normally we believed that we are safe is we avoid contact with the sick person but if we mishandle all the materials involved on treatment we can be infected by  the same pathogens.

It is important to have the correct information about disposing material and ask question if any doubts. its never smart to assume !