Bromate in high levels over a period of time can cause cancer. It does not immediately cause sickness when swallowed.
I would still take precautions when ordering a frozen drink where alot of ice is used. It is a good idea to use bottled water for making coffee and when brushing your teeth just pour mouthwash on your toothbrush and also floss. The question if the restaurants will take this Bromate threat seriously is anyones guess. Drinks straight up no ice and food choices that would not require water is a good idea.