The sun bends the trajectory of light slightly. And a black hole will bend the trajectory entirely. This is all dependent on the proximity to the source of gravity. For a given angle, is there some minimum mass required to bend light light at least that much?
I believe you've already spotted the answer to your question with this sentence:
And a black hole will shift the trajectory entirely. This is all dependent on the proximity to the source of gravity.
You can "shift light" (bend its trajectory) as much as you want with as little mass as you want using a black hole. Just let the light get arbitrarily close to the event horizon. There isn't any (practical) lower limit on the mass of a black hole so there isn't any particular mass required to bend light. Just huge densities which will cause the curvature of space needed.