this is funny and scary...but on a more nerdy note the long term average inflation rate for the dollar over the last 100 years or so has been 3.22%. So prices double roughly every 22 years. Going purely by the math, they would be a 1000x in 220 years or so...so this event should definitely happen between year 2240 - 2250 

But unlike fiat currency, whose money supply is continually added, bitcoins are fixed at 21 million. Assuming bitcoins were to keep increasing in popularity and acceptance and the user trajectory keeps increasing and assuming a 5% inflation rate (i just pulled this from my hat), prices would double every 15 years, so in another 150 - 160 years we would get there or by year 2165 - 2175.