、。
She's busy at the moment, so she can't speak with you.
Literal
She [topic-は] now busy-and, you [with-と] honorific-talk cannot.
忙しく is the i-adjective continuative form (the く-form), used here to chain into the next clause without a connector — equivalent to a comma plus 'and' in English. It works much like the te-form for verbs, letting two clauses share a subject and unfold sequentially. お話する is humble polite: the prefix お+masu-stem+する is a productive humble pattern that lowers the speaker's own action (or that of the in-group) relative to the listener. お話できません is its potential negative — 'cannot honorably speak.' Note the omitted subject for the speaker's reasoning is implied: 'because' is built into the bare く-form.