James,
I would want to check to see if the paint that splattered on your bike has any "abrasive" in it..often times "line" stripping paint has reflective particles that can be abrasive in it in order to make the lines glow in the dark.
Try shinning a light on it while the bike is in the dark...if the speckles glow it contains a grit and may scratch the paint if you are not careful when trying to remove it...light rubbing with liquid of choice while folding the rag with every swipe.
Best, Ben