If light is a constant and gravity bends light then light should speed up, slow down or both?

The speed of light is a physical constant. The only time it changes speed is when traveling through a different medium.

Gravity does not bend light. Rather gravity warps spacetime and light continues in a straight line through the bent space.

"Bending" does not imply speeding up or slowing down, and gravity does neither to light. It still moves at 3 x 10^8 m/sec.

Gravity "bends" space-time" the light follows the curvature of the space-time at the speed of light.

I do not know at which level you are . Here I give you the most general answer.

Gravity is not a force. It is a geometric property of spacetime. Space time fabric bends/gets curved due to the presence of a heavy object and this effect is known as gravity. This is the outcome of Einstein's General Theory of Relativity.

Now when a light beam passes nearby the space of a big star, suppose , sun, the path it takes in the curved space is the one which is called Geodesic. It is the shortest path and a straight one, the action integral (Advanced classical mechanics) is minimized for this path. If there were no bending of spacetime, the light would have travelled in a straight line but this straight line appears to be curved due to presence of a heavy object.