Can viruses that normally infect eukaryotic cells also infect bacteria?
I'm not so sure about my answer. But I think "bacteriophage" is a polyphyletic name of which was defined by the ability of infecting bacteria, but not defined by the genetic, evolutionary, or morphological relationships. 

It seems that if a species (or a taxon in a higher taxonomic level) of virus is infectious to bacteria, it will be classified as a member of the bacteriophage.

Here is a review article about the phage classification.