To use a bike odometers as wind meter is necessary define how many pulses per meter/sec are required to be shown in the odometer that reads the equivalent to MPH or KPH.
Most odometers have 1 pulse per wheel revolution and with the wheel diameter input into the odometer then the equivalent velocity is displayed.
Assuming a 26 inch diameter = Pi*D = 3.14 * 26 = 81.68 inches = 81.68 * .0254 meter/inch = 2.07 meter per wheel revolution.
At 0.1 meter/sec the equivalent KPH is 0.1 m/s * 3600 sec/hour = 360 meter per hour or 0.36 KPH.
At 1 m/s then the display will show 3.6 KPH = 2.2369 MPH.
So to obtain a practical reading, the odometer ( internal odometer capabilities) needs to receive 10 pulses per revolution of the anemometer wheel, and mentally divide by ten which can be done moving the dot to one place to the left of the display.
At 0.1 m/s the wind has extremely low power and it is difficult to have a wheel that turns well, so here is the main problem that if it is solved, then the pulse detector needs not to present a load to the anemometer and in this case the easiest way is to use a wheel with 10 holes for a photo sensitive detector to receive the light interruptions the dark material of the wheel presents during the rotation of it.
Anemometer wheel requires a extremely low friction bearings, mostly like the bearings that a micro-ampere D'Arsnoval movement may have and of course protected from higher winds that may damage the bearings.
Another one is a magnetic bearings but that is another project with its own difficulties and behaviors.
Good luck with your experiment,
Nando