。
As soon as she saw me, she ran off.
Literal
She [topic-は] me [object-を] sees [when-と] immediately ran-off.
The pattern ~とすぐに combines the temporal/conditional と ('when') with the adverb すぐに ('immediately') for an emphatic 'as soon as' — tighter and more vivid than plain と alone. 走り去る is a compound verb pairing 走る ('to run') with the directional/distancing auxiliary ~去る ('to leave, depart from'), yielding 'to run away, to run off into the distance.' The pair ~去る / ~帰る are common compound-verb suffixes for departure direction.