The answers before me work pretty well, but I'll throw another in: Get over wanting whatever you are building to be pixel perfect to what you have mocked up.
Assuming you are using the 12 column layout in 960.gs, then you are golden, because Bootstrap 3 uses a 12 column layout. Are the columns and gutters the same width as 960? Probably not. But I can guarantee that the screen your users are going to use to look at the website is not going to match whatever setting you have going on in Photoshop, either.
Not to mention the fact that once you (or your users) begin generating content, your perfectly crafted content boxes with the perfect number of characters will start stretching and shrinking in more ways than you can think of.
So you shouldn't worry if 960.gs can equal Bootstrap, because the real world isn't going to match Photoshop. Download Bootstrap, start coding your website, and be flexible about it not being pixel perfect to your current vision, because it never was going to in the first place.