¿Cómo se dice en español? Took a chance.
The sentence in English is: She took a chance and asked him if he was busy that night.
2 Answers
To take a chance has the connotation of risk, so I would use arriesgarse or tomar el riesgo in this context.
Aprovechar de la opportunidad is closer to taking advantage of the opportunity.
I would say:
Aprovechó la oportunidad y le preguntó si estaba ocupado aquella noche.