It was most likely Jirachi that turned you into a Pokemon mainly due to the plain reason that it is the granter of wishes. Seeing as Bidoof yearned for a friend such as you, it only costed Jirachi one ounce of power to make the wish come through. However I don't believe this was intentional seeing that it is in it's power to grant wishes but that does not necessarily mean it has the power to free-willingly twist ones faith. I would say it was rather a coincidence that you were the one to transform...perhaps because of the unique traits Bidoof may have requested and that you were the only one to meet the criteria
I do believe that it was by all means not Darkrai that turned you into a Pokemon. It was Bidoof's dream to have a friend such as you, however Darkrai does cause nightmares if it is in it's will or not. Darkrai's main legendary powers lies in the fact that it can make a dream which is pretty much what enables us to see the next day into a nightmare bringing fear in many peoples hearts
So yeah, I believe it was Jirachi that made the magic happen.