why is light bent by black holes if light does not have mass?

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Well, without going into a full description of general relativity and the 
physics of curved four dimensional space time, I think that the best 
thing to say is that energy has an equivelant mass. In other words energy 
behaves as if it had mass given by
                         E
(1)                 m = ---
                        c^2
                         
Where E is energy, c is the speed of light and m is the equivelant mass.  
Thus if you had a box with perfect mirrors on the inside and trapped a 
bunch of photons inside it the box with the photons in it would weigh 
more than if the box had no photons in it. (The extra weight however 
would be very slight.)

What you would be weighing is energy!  Anyway the answer to your question 
is that even though photons do not have mass they do have an energy 
equivelant mass which is affected by gravity.  Thus all objects that 
carry energy, including photons, ie light particles, are affected by 
gravity.  thus a black hole or any gravitating mass for that matter will 
bend the path of light.  Hope this helps.