There's 2,082 Narcissus listed on the KAVB site, but the RHS has the International daffodil register.
http://kavb.back2p.soft-orange...
There's a contact email for the daffodil register, I wonder if they would be willing to give a list. I found you can get it but it costs £40! The three supplements on top of that cost £5 each but there's downloadable links to those for free.
http://www.rhs.org.uk/Plants/R...
The RHS search link for daffs..
http://apps.rhs.org.uk/horticu...
If anyone else is looking they can get info on Dahlias, Hippeastrum, and many more bulbs.