The thing is, individuals and institutions worldwide currently own around $300 trillion in financial assets.[a] If as a group they decide to hold, say, 2% of their financial wealth in Bitcoin, say, to diversify away from all nations on earth, then Bitcoin's market capitalization would go up 30x, from around $0.2 trillion to $6 trillion. The number of bitcoins is fixed, so the price would go up by the same multiple. In short, all it takes is for the world to want a tiny exposure to Bitcoin.
Note that before Bitcoin it was impossible to diversify away from all nation-specific risks.
[a] http://money.visualcapitalist.com/worlds-money-markets-one-v...