How fast does MgSO4 absorb water from the air?
This is a great question, and unfortunately, I don't have an answer for you.

My first instinct would be to question how well you heated the material and under what conditions. Insufficient heating would mean that you might still have water remaining in the material.

Anhydrous, powdered magnesium sulfate will absorb water relatively quickly at ambient conditions, though it will depend on the temperature of the solid, how anhydrous it is and the humidity of the air. Something more to consider is that the crystalline form will absorb water at a slower rate. Were you dealing with powder or crystals?

Unfortunately, it isn't possible to judge the kinetics without more information. Perhaps you can provide your procedure?