For example, would it be considered right if I said "I already gave you the money, Bob!" when I gave him Bitcoin?
Money is something that is used as
- a medium of exchange
- a unit of account
- a store of value
in a given socio-economic context.
In the context of the Bitcoin community, Bitcoin is being used as a medium of exchange (payment vehicle) and – as the existence of "hodlers" shows – as a store of value.
You apparently agreed with Bob that some specific amount of Bitcoin would be sufficient to repay your debt to him. Therefore, you are denominating your debt in Bitcoin, i.e. using it as a Unit of Account.
Under these circumstances, both Bob and you should consider "I already gave you the money, Bob!" an accurate usage of the term money.
In other circles, there is discussion especially about whether Bitcoin fulfills the "Unit of Account" property. Hence, others may disagree that Bitcoin is money.