My understanding is that bridges are implemented via application services (the Matrix term for privileged plugins that extend the capability of the server,) so a user's ability to communicate over non-Matrix protocols is dependent on the homeserver where their user account is based. The best known example of this is that the public matrix.org homeserver is bridged to the Freenode IRC network, and certain channels are synced to each other, e.g. (#matrix on Freenode is the same thing as #matrix:matrix.org on matrix.org.)

I'm not sure how this works for non-public communication, like private messages on IRC or services like Facebook where it wouldn't be safe for the Matrix homeserver to have access to a user's Facebook account.

At this point I'm not super well-versed on the details of application services so hopefully one of the Matrix team members will reply to you directly.