Tor's man page currently documents the BridgeDistribution option as:
BridgeDistribution string If set along with BridgeRelay, Tor will include a new line in its bridge descriptor which indicates to the BridgeDB service how it would like its bridge address to be given out. Set it to "none" if you want BridgeDB to avoid distributing your bridge address, or "any" to let BridgeDB decide. (Default: any) Note: as of Oct 2017, the BridgeDB part of this option is not yet implemented. Until BridgeDB is updated to obey this option, your bridge will make this request, but it will not (yet) be obeyed.
Similarly, dir-spec.txt says about bridge-distribution-request:
All bridges SHOULD include this line. Non-bridges MUST NOT include it. (It is currently ignored by Bridge DB.)
BridgeDB however implements this option since 0.5.0, see #23957 (moved). I'll push a fix for these issues in a second.