I never exercise during the middle of the day for that very reason - don't want to overwash my face.
If I exercise in the morning, I wait until after I've finished exercising to wash my face and get ready for the day (then again, I don't wash my face in the morning, I just splash with water; I only wash my face at night).
If I exercise at night, I do so right before I'm about to shower/get ready for bed, that way I'm never overwashing.
Then again, I don't leave my house to exercise. I find room in my house to do it...I find I exercise better when I'm alone...So I'd recommend possibly doing that for you, too...See if you can find some space to privately exercise with the use of music/exercise DVDs or VHS's...