Just skimmed over your shader but this part looks odd and is probably where things go wrong:

if(N.x == 1.0f)
  p1.y += 0.5f;
else
   p1.x += 0.5f;

Shaders that use normal(!) mapping typically require a face normal and a tangent to work. The tangent is parallel to the surface and always perpendicular to the normal and exported meshes that are UV mapped should have one by default.

When implementing bump mapping you should also make use of the tangent. You can take a normal mapping shader as a reference. The only conceptual difference is that instead of sampling once to get the the normal of a fragment you sample the bump map multiple times in the direct neighbourhood. From the difference between samples you calculate a gradient along the tangent and along the binormal (binormal = tangent cross normal) and based on the gradient you skew the normal to receive the bump effet.

Solution B: Convert your bump map to a normal map using Nvidia's Texture tools. https://developer.nvidia.com/nvidia-texture-tools-adobe-photoshop

Try this:

float3 GetBump(Pixel input)
{
 float3 N = normalize(input.Normal);
 // Calculate the size of a single pixel in the bump texture.
 float2 bumpTextureSize;
 BumpTexture.GetDimensions(bumpTextureSize[0], bumpTextureSize[1]);
 float2 pixelSize = 1.0f / bumpTextureSize;
 float2 uv = UVTransform(input.UV, BumpTextureScale, BumpTextureRotate, BumpTextureTranslate);
 // Get the height value of this pixel.
 float3 mid = BumpTexture.Sample(TrilinearSampler, uv).r;
 // Get the height values of all neighbouring pixels.
 float left = BumpTexture.Sample(TrilinearSampler, uv + float2(-pixelSize.x, 0)).r;
 float right = BumpTexture.Sample(TrilinearSampler, uv + float2(pixelSize.x, 0)).r;
 float top = BumpTexture.Sample(TrilinearSampler, uv + float2(0, -pixelSize.y)).r;
 float bottom = BumpTexture.Sample(TrilinearSampler, uv + float2(0, pixelSize.y)).r;


 // Calculate the amount of height difference.
 float3 p1 = ((bottom - mid) - (top - mid)) * normalize(input.Binormal);
 float3 p2 = ((left - mid) - (right - mid)) * normalize(input.Tangent);


 // Calculate the final offset to add to the normal.
 float3 No = (p1 + p2) * -BumpDepth;


 // Add the offset to the normal and normalize it.
 float3 Nn = normalize(N + No);


 return Nn;
}