> Would it maybe be better to split this method into two? 

Why not but I am not sure what it brings you. I suspect that in many situations, this is one and the same logic. So that would lead to duplication of code.

> why pass the member as a string? Just for logging?

Yes that's the use case.

> Would it make sense to parametrize the interface?

I am not sure why `supportedBridgeTypes()` returns a subclass of `Annotation`. What do you have in mind? Say I have a bridge that can index `Address`. There is no annotation involved.

> in case we think a provider can handle multiple bridges.

I think that will be the case.

> Regarding _ AnnotatedElement bridgedElement_, I think I'd rather see Map to pass just the properties of the annotation

The provider if in need of one or several annotations would need to declare them statically? And `returnFieldBridgeIfMatching` would receive a `Map<Class<? extends Annotation>, Map<String, Object>>`? What about nested annotations? Is that what you had in mind?