BSDs is an acronym for branded short domains. A branded short domain is a custom 15 character or less domain for bitlinks. This allows you to customize the domain to your brand.
See the full Bitly API documentation for BSDs.
With an API client you can list the BSDs available to the authorized user.
client = Bitly::API::Client.new(token: token)
bsds = client.bsds
Or with the class method
bsds = Bitly::API::BSD.list(client: client)