Bromite deposits can be found on Home Island, Spirits Island, and Whisper Island. Clearing them will get you bitumen and stones – the bigger the deposit, the more bitumen and stones you will get.
Bromite deposits will regenerate after you clear them. For more information on how and where they regenerate, see the article Do Resources Regenerate on Home Island?.
If you want to find out more about where you can find Bromite deposits, check out the Archipelago Islands section.