Amazon has
Public Data Sets on AWS. I don't know the current status, but it used to be free for eligible projects [1].
BitTorrent would be the natural thing to do, but it has it's own set of issues. Jeff Atwood summarized them nicely in [2]. This was written in 2009, LegalTorrents doesn't exist anymore and you don't need a tracker anymore, but the rest of the points are still valid.
His summary is:
> It's ironic that BitTorrent, which is justly famous for equalizing the highly asymmetric nature of most people's internet connections, is itself so asymmetric when it comes to sharing: trivially easy to consume, but awkward and confusing to share. That's too bad, because BitTorrent is such a powerful tool for sharing. Hopefully this post demystifies the process a bit!
[1] http://phx.corporate-ir.net/phoenix.zhtml?c=176060&p=irol-ne...
[2] https://blog.codinghorror.com/sharing-files-with-bittorrent/
EDIT: Thinking about it, there is no shortage of free public data sets. I believe many of them are provided by individuals and organizations which wouldn't be able or willing to pay the bandwidth cost out of their own pockets. Maybe you could research the solutions they are using. A starting point could be the [3].
[3] https://news.ycombinator.com/item?id=2165497