Silver is not chemically inert. Various acids, cosmetics, and other substances, even mild ones, can affect it. Also, even sterling silver is an alloy containing other metals to make it more durable.
You can try polishing your bracelet just as you would silver forks and spoons. Use a rouge cloth or silver polish.
If the discolored area is small, and on the underside where it won’t show much, you could apply colorless nail polish to isolate the silver metal from whatever it is on your skin that’s causing the problem. (Do that after you’ve removed the stain.) People who are allergic to the nickel in some gold alloys often do this with their rings.