She used to visit me regularly.

Literal

She [topic-は] regularly me [object-を] visit-come [used to-ものだった].

~たものだった marks nostalgic reminiscence — 'she used to (in the past).' たずねてきた uses ~てくる for directional motion toward the speaker: she came to visit (toward me). 定期的に provides the regularity. The combination paints a picture of a past routine the speaker remembers fondly.