The fundamental value of the bitcoin system is the value of all the trades enabled by it (minus all the electricity burned). Unfortunately this is hard to estimate - because of two things: we don't know which part of a bitcoin transaction goes to the new owner and which is just the rest going back to the original one, and we don't know which of the transactions are truly non-zero-sum trades and which ones are just speculations. My intuition is that 99% is speculation (and the rest is mostly drugs).

Once we establish the value of the whole system - we can divide it by the number of bitcoins in circulation and get the fundamental value of BTC.