bent on...

「〜しようと考えている、するつもりである」

bent on...の後に、名詞や...ingを続けます。例文では、「公共物破損行為や暴力に訴えようとしている人たちは〜」という意味で使われています。

CNNの記事、'G-20 protests plagued by violence, vandalism'から。

'Police fired tear gas Sunday to tame groups protesting the arrest of G-20 demonstrators in Toronto, Canada, said Nena Snyder, a spokeswoman for the Integrated Security Unit.

An old film studio was converted into a prisoner processing center specifically for handling G-20 protest arrests. Police released tear gas outside that center where other people were protesting the arrests, Snyder said.

"I do not believe that the individuals bent on vandalism and violence in our city have finished with their intent, so we will remain vigilant," Toronto Police Chief Bill Blair said Saturday night'.

ちなみに、vigilantは「用心深く、警戒して」という意味の形容詞。