She had heard the story before, so she didn't want to hear it again.

Literal

She [topic-は] that story [object-を] before [time-に] heard [past-experience-ことがある] [because-ので], it [object-を] again hear-want-not.

~たことがある is the standard construction for marking past experience — the speaker has done X at least once before, framed as a fact stored in memory rather than a one-time event. Pairing it with ので ('because/since') chains experience to consequence: known story → no appetite to revisit. The desiderative ~たい flips negative as ~たくない ('don't want to'), inflected like an i-adjective. The whole sentence reads as third-person interior reasoning, the kind of summary you'd find in a novel.