She suddenly burst into tears on hearing the news.

Literal

She [topic-は] that news [object-を] hearing [then-て], suddenly burst-out-crying.

急に ('suddenly, abruptly') is the more conversational counterpart to the formal 突然 — both mean 'suddenly,' but 急に is the everyday choice. 泣き出す is the same compound verb 'cry-burst-out' (from 泣く + 出す) for sudden eruptive crying. The te-form 聞いて links cause to effect; the comma adds a brief pause before the reaction, slightly heightening the sense of suddenness. A clean, unembellished sentence that contrasts with the more elaborate variants.