Is it possible to create a pinterest-like layout with Bootstrap only?

Found a (free) template at http://bragthemes.com/demo/pinstrap/. It's supposed to have all you are asking for. Haven't had time to check it out, though.

Edit 2016-03-15: Bootstrap 4 allows this out of the box here. It's still in alpha, but we're getting there.

Found this solution, works within bootstrap (works even without defining column sizes), doesn't require javascript -- I snapped it into a project and it works beautifully:

http://www.bootply.com/118335

Bless you @katiejones!