I'd agree with the fairly detailed responce by EngineerTex, but would also add the following for consideration.
Generally, there must be some amount of gap between the bushing and shaft. Let's assume first that the bushing is infinitely stiff such as if it were pressed into a housing of the same thickness as the bushing. In this case, the shaft's bending (ie: deflection) at the point where the transverse hole is, is restricted by how much clearance is available. Imagine a small clearnance and then imagine imposing a bending load (as you show in the picture) such that at first, only the two outer edges of the bushing are in contact at the top of the bushing as shown in the picture.
As the load is increased the shaft bends into a U shape with the center of the shaft coming down and contacting the opposite (lower inside surface) of the bushing. Further increase in load tends to flatten out the shaft in the center as it pushes against the lower surface shown in the picture - such that along this flattened, center section, stress is essentially zero (assuming the bearing is infinitely rigid). This probably won't happen, but by assuming a constant moment between the two edges, you can find the point where the deflection takes up all the gap between the bushing and shaft. An increase in the bending moment won't flatten it much, though you could continue this by assuming the shaft is cantalevered at some point just off center such that the imposed load causes the shaft to touch at the top of the bushing.
If you look at the stress created by this known deflection, you could then apply the stress concentration to that value. Note this is assuming the deflection calculated is less than the deflection as if it were a point load at each end of the bushing and a constant moment between them.
This all assumes an infinitely rigid bushing with no wear, so the next step would be to try and quantify how much additional deflection will result as the bushing material is compressed around the point loads. Also, as the bushing wears at the contact points, the shaft deflection will increase. So it could be that stresses are within the infinite life range for the material, but after some material is worn away from the bushing, deflection increases, resulting in increased stress and eventual fatigue failure.