She has her hair tied up in a bun.

Literal

She [topic-は] hair [object-を] [round-丸く] is-bundling.

丸く is the adverbial form of the i-adjective 丸い ('round'). Modifying 束ねる ('tie up, bundle'), it gives the shape of the bundle: 'in a round form.' The ~ている describes a resulting state (her hair currently is bundled this way).