Well let the speed of light be c, the speed of the bus be b the distance to the mirror m.
Than the time t for the light to start at your body and come back to you is t = 2m/c.
Further the bus driven in this time a distance of a = b*t
So the angle you watch yourself is
θ = atan(m/a) = atan(m/(b*t/2)) = atan( m/(b*2m/(2c)) ) = atan( c/b )