Not sure whether the definition of a bearer asset necessarily implies that it should be a claim against another, generally more valuable asset.

Bitcoin is money and as such it can be exchanged against all goods and services currently sold for Bitcoin, but it's not a claim on any underlying asset that somehow legitimizes it, as gold legitimized cash.

A bearer asset is in my opinion better understood through the lens of counterparty risk. Cash has counterparty risk since the fiat money supply can be increased or decreased in arbitrary ways.