Unfortunately, you are SOL. Since your box only has 1 black wire and 1 white you can't do what you want. Those 2 wires go directly to your wall switch. In order to do what you want, you would need a 3rd wire in the box that is not on a switch. The best you can do is to wire both your fan and light to the switch. Black and Blue on the fan to the Black in the box and White on the fan to White in the box. In order to work the fan and the light independently you would need to use the pull chains on the fan.
I have this problem in one of the rooms in my house and have learned to live with it.