Bridges can publish server descriptors (with contact info) in multiple ways. Private bridges are configured with
BridgeRelay 1
PublishServerDescriptor 0
and don't publish contact info at all (you have to manually give out the bridge address to someone who needs it, then only that person gets your contact info). However, you can also configure with:
BridgeRelay 1
PublishServerDescriptor bridge
to publish your bridge descriptor to the bridge authorities. From the Bridge Specification:
Bridge authorities are like normal v3 directory authorities, except
they don't create their own network-status documents or votes. So if
you ask a bridge authority for a network-status document or consensus,
they behave like a directory mirror: they give you one from one of the
main authorities. But if you ask the bridge authority for the
descriptor corresponding to a particular identity fingerprint, it will
happily give you the latest descriptor for that fingerprint.
So your contact info is only handed out to the people who use that bridge. They can also get the bridge info in other ways:
Bridge users can fetch bridge descriptors in two ways: by going
directly to the bridge and asking for "/tor/server/authority", or by
going to the bridge authority and asking for "/tor/server/fp/ID". By
default, they will only try the direct queries. If the user sets
UpdateBridgesFromAuthority 1
in his config file, then he will try querying the bridge authority
first for bridges where he knows a digest (if he only knows an IP
address and ORPort, then his only option is a direct query).