My understanding, and a few thoughts ...
Bhakti Yoga is essentially losing oneself, or one's attachment to a 'self' through devotion to a spiritual higher power, a god, whatever you want to call it. It's like the drop of water that retains all of its qualities, yet loses it's separation from the big scheme of things when it falls into the ocean.
In that respect, it could be argued that Shin Buddhism is a kind of Bhakti yoga, because by relying completely, or taking complete refuge in infinite mind (which is characterized by Amida Buddha) one lets go of the finite mind of delusion, the source of suffering for beings.
The essential difference, I think, is that Bhakti yoga's premise is one of being united, or reunited with something we can call "the divine" whereas in Buddhism, one was never separated to begin with. Instead, merely the arising of confusion has occurred as a result of self-grasping, and so we do not see our true nature.
But, if Nembutsu practice were truly Bhakti Yoga, one would have to keep practicing until one achieved oneness with Amida. But this is self-power, which is dismissed in Shin Buddhism as futile. Instead, it is through the principle of Amida's vow by which one is already established in the Pure Realm. In other words, Because the true nature of mind is infinite already, there is nothing to gain (as there would be in Bhakti Yoga) , merely, in gratitude, only something to realize.
I think this sort of Bhakti-style Buddha-worship did arise now and then over the centuries, and was dimissed as being basically a misunderstanding.
Profile Picture: "The Foaming Monk"
The Chinese characters are Fo (buddha) and Ming (bright). The image is of a student of Buddhism, who, imagining himself to be a monk, and not understanding the true meaning of the words takes the sound of the words literally. Likewise, People on web forums sometime seem to be foaming at the mouth. Original painting by P.Volker /used by permission.