I tried doing a "View source", but couldn't figure out how to definitively know whether a given website built with Bootstrap or not. (Also tried a Google search before posting on HN.)
Markup is the way to go, look at classes of buttons, divs and spans. Look for <i>-lg or span</i>s and stuff like that.<p>That... and you could open up the dev console
Checkout <a href="http://builtwith.com" rel="nofollow">http://builtwith.com</a>. If the css is not renamed, merged or minified it will be listed in the technologies used. Else, you have to do the one of the other suggestions here.
I'd also like to suggest a really cool browser plugin called Wappalyzer. Its really good (ok, kind of decent) at guessing the platforum of a website and will even guess plugins, frameworks, CMS, web server and I think sometimes even host.
A mildly decent way is to check for `span[0-9]+` or the newer `col-` whatever classes. A site using classes of `container` and the ones previously mentioned probably has a 80%+ chance of using the bootstrap grid.