There are bloody parts of the New Testament. Most of them are in the book of Revelation/Apocalypse. Then there are the beheading of John the Baptist and the slaughter of the Holy Innocents of Bethlehem.
The Christian Church also accepts the Old Testament in its entirety. Our relationship to the bloody parts of it would be too long a discussion for the time that we all have.
However, the Bible nowhere counsels killing the "infidels" wherever you find them (in any time or place), conquering the world by the sword, and other such features of the Qu'ran. It is true that many muslims do not emphasize these teachings of islam. But many others do, and contrary to what we are hearing from many of our political leaders, they are part of mainstream islam.
This woman is a foreigner with no real feeling for our country or our way of life. She has a European sensibility and identifies with Europe; that's why she travels there to criticize America before foreign audiences: something unprecedented in our history, something Clinton's other Secretary of State--Warren Christopher-- does not and would not do.