Short period of exposure to asbestos?

Asbestos related cancer won't show up for 10, 20, 30 years after asbestos exposure. No one knows how much exposure puts you at risk. It exists in airbourne, fiber, and liquid I believe.

We really do not know the lower bounds of exposure that causes problems.  It may be one fiber if everything goes wrong could cause a problem.  What we do know is that the lower the dosage, the less risk a person has.  And yes, moist air will keep exposure down.  That is why asbestos is wet down when removed.

Now you have to be careful talking about "asbestos" being only in fiber form.  There are really hundreds of minerals called "asbestos", not all make fibers.  There are six "regulated asbestos" forms that do exist as fibers if processed and used in building materials. However, in building materials such as cement, you have to sand the material to release fiber forms.  As the natural mineral, they look like a rock and may or may not have fibrous forms showing.

Asbestos is very unique in that the fibers are microscopic and when inhaled, can pass through the lining of organs like the lungs and leave perforations that lead to the thickening of pleural fluid in and around the lungs. These fibers can also lead to cancer of the Mesothelium, which is commonly referred to as Mesothelioma...

It takes years and years of exposure to air born asbestos fibers to potentially cause damage to a human system.  Even if you were exposed for a number of months, you have little to fear.