You might think it strange that fabric or clothing could cause acne - but this about it in this way. Say you have a helmet that you wear for 12 hours straight on a bike trip, and that there's a chin strap on it. Say that chin strap covers up 10 pores on your face. All of those pores are making oil - but the oil can't get out. It is stuck in the pore. It dries up there, gets crusty, and forms a seal. Now when more oil is made, it is stuck and makes a bubble. The bubble of oil gets infected, and now you have acne.
It's important to only have LOOSE clothing on if you're having an acne problem. This of course can't be helped with a helmet - helmets have to be worn snug - but you can at least take breaks and carry a face wipe to use during the breaks. Keep your collars loose.
Here's an interesting thought for you. Every night when you go to sleep, you probably mash your face into your pillow. Maybe you lay on your side so that half of your face rests on it, pressing into it. All of the stuff on your face - the dirt and so on - is now pressed against your pores for multiple hours. Also, if you have anything on your hair - gel, shampoo, conditioner, dirt and grime - all of that will get squished into your face as well.
You can help greatly by washing your face before you go to sleep. That at least will give you a fighting chance of having your face still be OK when you wake up. Also, as much as a pain as it might sound, replace your pillowcase each night. That only takes maybe 30 seconds to do, and hardly adds to laundry at all. The benefits, though, can be immense. It means if you have a clean face and clean pillow, that you have as low a chance as possible to cause issues for your skin.