For example, if a single beam of light was directed directly at the tangent of a semi circular mirror, would it be considered bending or redirecting many times to form a near circular pattern? When I say bend I mean in a curved trajectory, not at an angle.
The phenomenon you're describing, of light being bent, is observed when light passes through a medium with progressively increasing, or decreasing refractive indexes.
You actually observe it when you see a mirage. When it's very hot, the temperature being progressively higher as you approach the ground, the refractive index decreases (because density decreases) and light coming from the sky is bent upwards explaining why you see "water" on the ground when it's very hot. When in fact, what you actually see is light from the sky being bent upwards into your eyes.
Hope my answer helped! :)
This image sums it up pretty well
a beam of light can be bent through an angle by sending it through a wedge-shaped piece of glass, requiring neither gravity nor reflection. this phenomenon is called refraction and can be studied in detail on wikipedia.
if a single beam of light was directed directly at the tangent of a semi circular mirror, would it be considered bending or redirecting many times to form a near circular pattern?
The problem with this plan is that it's not possible to make an infinitely narrow beam of light. Because of diffraction, the diameter of a beam of light is limited to roughly the wavelength of the light. And if you try to make a beam with a diameter close to this limit, it will diverge very quickly. To make a collimated beam (one that doesn't diverge very much), you have to make the diameter of the beam substantially larger.
So there's no way for all the light to travel exactly tangent to the mirror surface, and the end result will not be the light beam skimming along the surface to exit the other side of the hemisphere. Exactly what will happen depends on the exact shape of the mirror and the beam profile. You normally wouldn't try to understand this problem analytically but just use a computer simulation to approximate the result.
To answer the question in your title,
can light be bent?
If you want to bend light, then it's more easily done with a prism or lens, or possibly gradient index optics, as described in another answer.