So if Photons don't have mass, then why are they bent towards a black hole?
(They don't have rest mass. But that distinction isn't really relevant to your question.)
I'm sure this has been asked and answered in any number of Reg comment forums for stories like this one, but the short version is that photons follow the curvature of spacetime, This operates just as predicted by general relativity, as has been demonstrated by e.g. the Pound-Rebka experiment.