Yep, that's a problem. Used to be you could get a free account from DropDAV.com and use the WebDAV feature in Numbers. Now they only have paid accounts, though they are not terribly expensive.
There are other options. You can get an email to DropBox through sendtodropbox.com. It can be slow (depending on server load I've waited an hour for a file to show up) and not 100% reliable (though it's always worked for me). You still have to log into DropBox and move the file from the Attachments folder to the Public one, but it's doable.
Alternately, and kind of bass-ackwards, you can Mail the file to yourself, then use Open In... in Mail to copy the attachment to the DropBox app. This is probably the easiest way, though the least intuitive.