It's dependent on your humidity and temperature. Count the days off until you think it is dry...and double it at the very least! At my very low humidity up here in western South Dakota I often give a minimum of 30 days.
Remember, the wood will be absorbing much of the moisture and it will take time to cure that out of the cells, too.
Where ever you chose to leave the bow to cure out, make sure there is air movement. That helps a great deal, can't be overstated...airflow!