I've been sweating profusely in athletic activities for 6 decades and have always needed a supply of head and wrist bands. For riding, I wear at least a wrist band, and for longer rides, I'll wear both or stuff an extra one of each in a pocket or hang on the bike. A washcloth is also usually folded over my waistband or wherever, and I use that to dry off my head and helmet padding when I stop; I can also soak it in a fountain or stream to cool off.

A reminder that if you sweat a lot, you need extra hydration.