For Bismuth, I should think ICP would do the job, provided you can digest your particles. Would probably work using aqua regia or just HNO3 with some HCl added.

You can get relevant information here, to start with : https://www.inorganicventures.com/periodic-table

This will give you Bismuth content but for Oxygen and Chlorine, you might as well turn to CHON elemental analysis directly on the solids and compute back Chlorine proportion (or turn to Halogen dedicated techniques such a hyphenated combustion-IEC).