The “small-scale test” is being conducted to “gather community feedback and data to improve Bloodborne’s online experience,” according to the e-mail.
Currently, it appears the e-mail is limited to European users.
But if you didn’t get an e-mail, it looks like you can enroll using this page here. Thank NeoGAF’s NSider for sharing the link. It appears you can submit your information with a U.S. account, but we can’t guarantee it will get you in.
A launch date for the alpha was not mentioned. The full game is due out for PlayStation 4 in early 2015.