。
She did nothing but stare at me for a while.
Literal
She [topic-は] for-a-while [interval-の間] me [object-を] gazing [nothing-but-てばかり] was.
しばらくの間 ('for a stretch of time') is the slightly more explicit, writerly version of bare しばらく — combining the adverb しばらく with の間 ('during, in the interval of') to make the time-span explicit. 見つめる ('stare, gaze, fix one's eyes on') is heavier than 見る — it implies sustained, deliberate focus, charged with emotion. ~てばかりいる ('does nothing but') makes the staring exclusive: she wasn't doing anything else. The whole sentence describes a sustained, weighted gaze that could carry love, accusation, or simply puzzlement, depending on context.