Runny nose while biking
Well, this probably sounds gross and I'm kind of reluctant to say it, but I'm able to blow the snot out of my nose without hitting myself or my bike.  I try to only do it when there's no one around, but occasionally that isn't possible.  Basically, I turn my head so my nostrils are towards the ground and exhale forcibly through my nose.  I'm not sure it will work for everyone--perhaps I have remarkably straight nasal passages?