Usually used in bent on, this meaning describes a firm and sometimes unreasonable determination.
She is bent on winning the competition.
He seemed bent on causing trouble.
This informal meaning describes a person, especially an official, who is corrupt or criminal.
The investigation exposed several bent officers.
He was accused of working with a bent official.
As a noun, bent refers to a person's natural skill, preference, or habitual direction of thought.
She has a natural bent for mathematics.
His creative bent was clear from childhood.