Hello and welcome! Have you taken the bridge out to make sure there are no screws showing at the bottom of the posts? The screws are not really visible from the top of the guitar.
Here's an example of what you should see. (see the bottom of the bridge post)
If you're still looking for small parts (like screws and washers) after verifying they are not there I always recommend going to your closest guitar repair shop / luthier. They usually have a bin around with extra parts they use and will help you out at fair price.
