1) No stir bar in the world can create as large a gas/liquid interface area as when you manually shake the bottle (the larger the area, the faster the reaction)
2) Pressure is needed, as we more or less want to push oxygen into the safrole by force, oxygen bubbles will not have any desire to add to the safrole if you just let them bubble through the solution, also - see (1) above, such bubbles won't create any gas/liquid interface area to speak of.
