。
She got off the bus and ran toward him.
Literal
She [topic-は] bus [from-から] get-off-and him [genitive-の] direction [to-に] ran.
彼の方に ('toward him') uses 方 ('direction, side') to soften and generalise the destination: not literally 'to him' but 'toward where he was.' This ~の方 ('the direction of') is a versatile construction — also seen in comparisons (こっちの方がいい, 'this one is better'). 降りる takes から for the place you're descending from (the bus, a train, a mountain); never を with vehicles in modern usage.