"Bent on" is a phrase that means someone is determined to do something, often with a singular focus and intent. There are a number of synonyms that can be used in place of "bent on" to convey the same idea. Some of these synonyms include resolved, set on, determined, fixed on, committed to, and resolute. Each of these words communicates a sense of unwavering purpose and a determined mindset. Using these synonyms can help to add variety and nuance to your writing or speaking, while still conveying the same sense of determination and resolve that "bent on" does.