How bitcoin gets monetary value
Currencies get value from demand and supply not from governments backing them. Currencies have existed long before government's started stamping them out in their own name. The demand for a currency comes from the utility that it offers as a medium of exchange. Even pre-historic humans went out of their way to create currencies because they were useful.

Bitcoin has value because it is useful as a global, irreversible electronic medium of exchange and store of value. That is why it is in demand.