Thanks for posting your query.
I will be glad to be of assistance.
For your concern it would be best to use ciclopirox
oleamine shampoo thrice a week.
Also conditioning after the wash will be helpful. You can use a good conditioner.
Application of coconut oil thrice a week at night also will reduce the dryness.
If possible tie a cloth on your head before riding your bike so as to prevent further dryness.