I only have 1 hour playtime in my Pearl version (no badges yet), but I've already found five shinies: three Shinx, a Bidoof, and a Budew.
Unfortunately I ran out of Poké Balls when fighting the third Shinx, so I only caught four of them.
I'm beginning to think my game is bugged.
EDIT: And just caught another shiny Bidoof. Definitely keeping this save file?