How much does it cost to change bits of data on a computer? That's what happens with quantitative easing. Bernanke isn't calling up the printing presses to print $2 trillion in paper currency.
That's not how quantitative easing works. Quantitative easing doesn't fire up the printing presses. Bernanke can add $2 trillion into the system within 15 minutes, and no paper money is printed or manpower expensed aside from a few clicks on a computer mouse. Once you secure your financial system network, adding currency adds virtually no costs relative to the amount of currency you put into that system. You've already secured the network.
It's akin to Facebook's security system. It works the same regardless if it's 100 million users or 1 billion users.
$2 trillion in 15 minutes might be a wee bit of an exaggeration... considering the monetary base needs to, um, actually buy something, usually Treasury Bills. Which are managed by whole swath of administrators in the Dept of the Treasury (and could lead to printing presses -- for the T-Bills, anyway), as they're usually issued in bond series, etc.
The Fed prints money through an auction/market involving only privileged actors (a small number of investment bankers). The new money then changes hands a couple of times before being distributed wide enough to have the desired macroeconomic effects. By the time it reaches you our me inflation has already set in. In those intervening steps, profits are made that dampen the effects of quantitative easing, requiring that the fed spend/create more money than it theoretically would need to in order to have the desired effect. That extra money can be thought of an "economic rent".