Subjectivity is just who you are as a person: there's nothing to be done about that, you have to write from the perspective of who you are, and many excellent historians even think that (used wisely) it is a good thing that can make you do better history.

Bias is a word that inherently carries a negative connotation. It means "not being objective in a bad way," usually in a way that is either dishonest (not telling your reader where you're coming from) or self-deluded (you think you're being totally objective when in fact you have a giant blind sport because of your perspective). Subjectivity, used well, can help with some of the problems of bias by acknowledging their interest in a topic and who they are in relation to it