Shoot The Core
Check this site's database: a ton of links to freeware PC shmups and demos, homebrew (doujin in japanese) or commercial.
Use the search engine using the 'full game' filter to see only the freeware ones.
Check their forums for advice or if you have dld problems.
If you need some more advice, just visit some shmups dedicated sites such as: shmup.com (french site but we've got an english sub-forum, you've guessed that's my 'home' ^^) SHMUPS! (the reference english site for shmups)
PS: the games being in english or not isn't a problem 99% of the time as there's almost no text in shmups, so do not hesitate to dld japanese games (99% of the 'bullet hell' shmups are japanese anyway).