Power will be applied to the frictionless bike to accelerate it. Once the bike reaches a steady state speed, no more power is applied to the bike from the wind. To oppose this (assuming the bike is still stationary and you intent it stay stationary), you need force to counter the wind drag, but you don't need power because the bike is not moving relative to the ground (where the force is being applied).
A good rule of thumb is, if you can do the job with an inanimate object, you are not applying power. A block of wood or your brakes cannot apply power to anything. If you can do the same job with a block or your brakes as you can with your legs, then you are not applying power to the bike. From the bike's point of view, it doesn't know if it's your legs or a block of wood or your brakes that is holding it in place.
Your powermeter will read zero under two conditions:
- the force on your drivetrain is zero
- the drivetrain is not turning
This is because
power is
force times
velocity.