She got on the bus and parked herself in a front seat.

Literal

She [topic-は] bus [on-に] got-on [and-て] front [of-の] seat planted-herself.

居座る ('to sit firmly, stay put, plant oneself') describes settling in with no intention of moving — usually with a slightly negative connotation of overstaying or refusing to budge. The verb is built from 居る ('to be present') + 座る ('to sit'). Notice the sentence skips a particle before 居座る: 前の席に居座る would be the standard form with a locative に. The omission here is mild casual sloppiness or possibly a transcription gap.