I've been lobbying for the mimetype solution.

+1 ^{(populism != sanity)}

The bitcoin: URL scheme makes sense by analogy to mailto: but

It leaves the transaction info visible. Without a standard way to transport and encrypt it (re-invent https?!), you encourage data leaks which are likely to link people to transactions.
Is >35 chr long. bitcoin: (8 chr) + address (27 in base64, 35 in the standard form?) + amount etc.
Compare something like ht tps://txn.bt/b64id which is 20 chr, of which some cavalier folk will omit 8. Without a checksum, it's good for 1E9 transactions.
"txn.bt has not been registered yet and so available. This domain could be purchased but with no guarantee. Availability of domain name doesn't necessarily mean this can be purchased." -- http://www.nic.bt/twhois/whoiss.php
If it's available, that's a nice landgarb for some enterprising person to make another centralised service.
So you need a transport for the text containing/of the URL. I think in HTML-over-HTTPS is intended, and could work fine. Otherwise, you could offer a shortcut (.lnk) file for download but a) they are platform-dependent b) cautious people don't trust them c) do shortcut files have a mimetype?

Cool!

I have cooked up an email version,

One encrypted email from Bob to Alice requesting payment and attaching your file.
Another mail containing a copy of Alice's GPG keys so you can read the first mail.
Currently for the benefit of those happy to download and open an mbox file.
I suggest moving your ~/.gnupg/ out of the way while trying it, to avoid accumulating the cruft key.

Also may I suggest from my armchair,

HTH,