The same way they do it today, you deposit bitcoins into their bank instead of having them in your wallet. You have bitcoins sent to your bank account instead of your personal wallet (it would eventually happen anyway), the bank becomes responsible if they get hacked or lose the money (just like it is today), so it would be served to the masses as a solution for having bitcoins stolen from personal computers. The masses will most likely do this.
If a thief steals $250,000 in cash from you, you're hosed.
If a bank gets robbed and a thief steals your $250,000, just 5 minutes after you deposited it at the bank, the bank is hosed.
As more and more people make deposits, they'll have a base reserve that they can use to make loans against. When they make a loan they don't just send you the full amount to your bitcoin wallet, but keep it in their deposit accounts so that you only use what you actually need at a particular time.
Just like in the real world when people borrow $50,000, they don't withdraw it all as cash and go walking down the street with it in a big money bag. That would be foolish.
The reserves would have to be much higher than today because, a bailout is not possible of 10:1 lending, but they can still engage in the practice nonetheless and if they are careful of who they extend credit to and charge the correct interest rates, it'll work just fine and be profitable.
This is only during a period when they make credit cheap, once they make credit expensive and stop renewing loans, the money exits circulation and the price level will eventually adjust downward.
For example, lets say during a economic boom, they fully extend their 10.5 million coins into the economy, the price level doubles as a result, someone buys a house and now has a mortgage at the new price level.
After a few years they as the loans are paid off they don't make new loans, the money supply starts to shrink as a result of the coins exiting circulation and over the period. The price level slowly starts to drop and it will eventually be a lower price level than it was previously (because the 10.5 million coins + whatever they collected interest - defaults), say their total profits was 1 million bitcoins, so they now have 11.5 million bitcoins, bringing the remaining bitcoins to 9.5 million available.
The actual price level then reflects the same as if there are 9.5 million bitcoins, but there will still be a significant amount of loans that reflect the price level at 21 million bitcoins.
Loans remain for the original amounts even though the price level drops, this basically increases the principle of those loans, on top of any interest charged.
Currency is a whole different ballgame, mankind has been enslaved by monetary systems since the beginning of civiliation. The government doesn't need to get control of bitcoin, just the private banksters.
The government isn't in control of the US Dollar right now anyway, the privately owned Federal Reserve is.