She was about to get on the bicycle.

Literal

She [topic-は] bicycle [on-に] ride-let's [quotative-と] did.

The volitional form ~ようとする expresses 'try to do X' or, with past tense, 'was about to do X / was on the point of V-ing.' 乗ろう is the volitional of 乗る ('let's ride / I'll ride'), and the と+する frames the volitional as an attempt or imminent intent. The past form ~ようとした often carries the implicature 'tried, but...' or 'was about to, when...' — something interrupted the attempt. Spelled in full kana (のろうとした) the sentence has a slightly soft, narrative feel.