I know that my facial hair was causing me to have acne and bumps. So I got rid of them. After my bumps disappear black spots are left. Why?

May be comedones. Acne is caused by skin pores being plugged by tiny clumps of skin cells (the clump of cells is called a comedone). When there are no bumps or actual pimples and pustules, the acne-prone areas of skin will still have plugged pores. Maybe the black spots are actually the comedones in the skin pores. The best way to tell is to have a primary care doctor look at the spots.