US banks have FDIC insurance to protect deposits up to $250,000 [1]. To the extent that you trust the US government you can trust that your money is safe in a US bank up to the stated FDIC limits. Banks fail all the time. There have been 8 failures in 2014 so far and not a single penny of depositor money has been lost. You can see a list of every bank failure and the outcome here [2].

The simple and incontrovertible fact is that the US banking system is as close to 100% safe as you can get. Bitcoin isn't anywhere close.

[1]: http://www.fdic.gov/deposit/index.html [2]: http://www.fdic.gov/bank/individual/failed/index.html