。
She bought a bicycle to commute to school.
Literal
She [topic-は] school [target-に] attend [for-ために] bicycle [object-を] bought.
~ために ('in order to') marks the purpose of an action — the purpose-clause comes first, with the main verb at the end. The verb in the purpose-clause is in plain non-past form (通う), not past or progressive. 自転車 ('bicycle') is a daily-life staple in Japan: schools, train stations, and grocery stores are surrounded by bike racks, and 通学自転車 ('school-commute bicycle') is its own market category — built for daily, weather-resistant use, often with a basket, lights, and a generator. For middle and high school students, the bicycle is often the primary mode of getting to school, especially in suburban and rural areas where the walk would be too long but trains aren't convenient.