She smiles at me every time we run into each other.
Literal
She [topic-は] me [with-と] encounter [every time-たび] smiles-toward.
出会う ('to encounter') implies more chance than the standard 会う ('to meet'). たび ('every time') here lacks the に particle — both forms are grammatical. 微笑みかける means 'to direct a smile at someone.'