It's not the paint dust (residual pigment) that's of first concern; it's the organic vapors from the solvents carrying the pigments. Paint dust can be controlled using a filter between your paint source and the exhaust fan. Any fans used to exhaust organic vapors should be at least brushless to avoid the potential for fire. A bathroom fan ain't it. In addition, organic vapors are heavier than air, and will tend to settle in the lower portion of the exhaust hose, unless the booth fan is strong enough to push them toward the ceiling. Bathroom fans are designed to help remove odors and rising water vapor. I'm sorry, but I believe you need to rethink how to get the vapors outside. How come you can't get to a window? Just curious...
Gip Winecoff