How should I mount a 10 ft 2x6 as a wall shelf?
So, the good news is that you almost certainly have solid wood all above the window to fasten to. This makes it a good candidate for blind shelf supports. (Google, but rockler sells them...)

Alternately (and cheaper), you could have inverted L brackets. Paint the top legs wall color and you'll stop noticing them. Only your fussiest visitors would notice. It's up to you to decide how sturdy you need, but if you find that you haven't got enough to be comfortable, simply add a few more.