Different textbooks and instructors use different conventions. Serway and Vuille's College Physics (8th edition) uses upright boldface with an arrow on top: ##\vec {\mathbf A}, \vec {\mathbf B}##. Knight, Jones and Field's College Physics (2nd edition) uses plain italic with an arrow on top: ##\vec A, \vec B##. Griffiths's Introduction to Electrodynamics (3rd edition) uses upright boldface without an arrow on top: ##\mathbf A, \mathbf B##.
You simply have to make yourself aware of the conventions that your textbooks use. When writing assignments, it's probably best to use whatever your instructor favors. I suspect that in the US at least, it's probably usually simply an arrow on top if you're writing by hand, because it takes careful handwriting to distinguish between upright and italic, and between plain and boldface.