She went to Chicago by bus.

Literal

She [topic-は] bus [by-で] Chicago [to-へ] went.

で marks the bus as the means of transportation — the same で that introduces materials (木で作る), instruments (ハンマーで殴る), and methods (日本語で話す). For transportation, this is the standard pattern: 電車で行く ('go by train'), 飛行機で来る ('come by plane'), 自転車で通う ('commute by bicycle'). へ marks the destination with a slight directional flavor — 'toward Chicago' — distinguishing it from に, which presents the destination as a concrete arrival point. In modern usage the two are largely interchangeable for travel verbs, with へ tilting more written/literary.