So, I ran some finance calculations, and:
If bitcoin value goes to $10,000 and stays there forever, but USD keeps inflating at 3% every year, Bitcoin will be worth $1,000,000 in 150 years (but $1mil will only buy what $10k buys today)
If Bitcoin value goes up and stays at $10,000, but USD keeps inflating at the rate it has over the last few years, bitcoin will be worth $1mil in just 67 years.
Keep in mind that I picked the $10,000 figure as a conservative estimate of BTC capturing only 0.5% of the world's cash amount.
Now let's say inflation is at a slightly higher rate than the target, at 4% a year, which is I think reasonable with the increased spending, debt obligations, and possibly continuing troubles in the global economy (it's just 1% higher than the Fed's 3% target), and Bitcoin grows at an average rate of a normal stock at 10% a year. Meaning instead of growing to $10,000 (or 0.5% of use) and staying there, it actually continues to grow, with 10% more people adopting it every year. In this case, Bitcoin will be worth $1mil in 56 years, at which point it will be worth about $100,000 in today's dollars, having a market cap of about $1.7 trillion dollars. I don't know what percentage of the total world wealth that will be, since we don't know how much the world economy will expand by then.
If inflation is the same 4%, but bitcoin grows at the same average rate it has over the last few years, about 2x to 3x, or, say, 250%, it will reach $1mil in just 5.9 years, where its worth will be $810,000 per coin. HOWEVER, if that happens, it will have a market cap of about $11 trillion dollars, which tells me that it's pretty much not possible for bitcoin to consistently double or triple every year for the next 6 years. (Sorry latecomers, you may still have a massive return, but there are not many of those left)
So, where about is a reasonable number? No one knows, especially since bitcoins growth is expected to be rapid over the next few years, then level off to something more sustainable years from now, and dollars will continue to decline. While I can set up such a model, the extra detail provided by the variables will not counter the fact that all these numbers are coming out of my ass. But, if we wanted to rough it, and I know you guys want at least some estimates after reading all this, then:
Using 3.5% inflation, and 40% annual bitcoin growth (very reasonable, considering Small Cap stocks give 16%, and we're talking global adoption for currency, transactions, and investments here), gives us a $1million Bitcoin in 21 years, with bitcoin market cap of $8 trillion dollars, which right now is maybe half of all the world's wealth, but 20 years from now may be a fairly small (reasonably believable) part of it.
So there you have it folks. About 20 years for bitcoin to hit $1,000,000, if bitcoin continues being adopted and doesn't fail or get replaced along the way (with an error rate of plus or minus 10 years). For those wondering if you will ever see it in your lifetime, you have your answer.