If you accept the speed of light as a universal hard limit, then you wouldn't see your reflection, as the "light" from your body wouldn't be able to advance fast enough to ever reach the mirror to be reflected
If you don't accept the speed of light as a hard limit, then you would see your reflection, as the relative speed between you and the mirror is zero, so the light from your body would be moving at twice the speed of light. And as photons technically have a non-zero mass, they should be influenced by momentum.