Really the ability of eyes cannot be explained in some ways. But you said that you can't see any light reflecting from bed sheet but you can see bed sheet.Really it is about normal light rays. There is also a small amount of rays reflecting.
But the light coming from eyes is not just like normal light.Just think, can we see light coming from eyes of others ?
answer is no. So light coming from eyes is not visible to us and it have different characteristics. Eyes will show black if there is no reflection and reflection is happening on all other objects.
Read carefully and understand and like if satisfied