I remember Bump from its early days on the App Store, when it was one of the first "contact sharing" apps with a unique gimmick: where you simply "bumped" your iPhone to someone else's to share contact information. Since then, however, Bump has been steadily upgrading its app, adding lots of other sharing functionality.
And the app's latest update adds even more: In addition to sharing any files stored on your iOS device (functionality that was added in the 3.5 update), the latest update (3.5.3) adds the ability to share any files sitting on your Dropbox. All you need to do is hook up your Dropbox account, choose which files you'd like to share and bump away. Obviously, there are loads of ways to share Dropbox files already, but if you and a friend happen to both have Bump, that's one more thing you can do with it.
There's an impressive amount of functionality they're putting into that app. Bump is still a free download on the App Store.