Bitcoin is not money: it is not M0/M1. It can be traded for money or for other assets - barter. It may be treated as money, but it is not money.
It may overtake money as a unit of exchange, at some point, IMHO probably never (central banks will come up with equivalent functioning if and only if block chains stop taking days/weeks/months to implement on clients), but it is not money, now.
Any token that can be used to exchange goods and services can be considered "money". Some money is better (read: better store of value, widely accepted, used as legal tender to pay taxes) than others, depending on the specifics of the transaction it is used for.
These tokens can be physical placeholders (dollar bills) or virtual placeholders (debits and credits in a bank account, bitcoin).
M0/M1 is a grouping of extremely liquid forms of money. Bitcoin is also relatively liquid, so it wouldn't be too far-fetched to include it in M1 if it were more stable (read: if it had a government or large corporation backing it).