-Very similar logotype
-Signup form on the right, with huge signup button
-Tons of whitespace w/ 'floating' elements
-Footer styled very similar
-Same location on the page and method of promoting their paid product -etc
The overall homepage though I think looks nothing like Bootstrap's docs, if that's what you're implying. Also, Bootstrap, and GitHub, was not influenced by Dropbox. We just iterated on that stuff internally in a pull request and shipped when we were happy with it.
Either way, I don't think it matters. It looks good and clean.
Not trying to be critical by the way. I'm a huge fan of every company/framework/person etc mentioned here. I'm just really interested in the form, function and messaging of homepages.