In Appendix E in the spec, named "Comparison of Other Binary Formats to CBOR's Design Objectives" there are several comparisons - including BSON:

   [BSON] is a data format that was developed for the storage of JSON-
   like maps (JSON objects) in the MongoDB database.  Its major
   distinguishing feature is the capability for in-place update,
   foregoing a compact representation.  BSON uses a counted
   representation except for map keys, which are null-byte terminated.
   While BSON can be used for the representation of JSON-like objects on
   the wire, its specification is dominated by the requirements of the
   database application and has become somewhat baroque.  The status of
   how BSON extensions will be implemented remains unclear.

It looks closer to msgpack if anything, but with actual strings and bytes.