There is no set time for this process, it depends on the individual. 
 
I know persons who have felt the spirit and accepted baptism after a few short hours, others who took years to become converted. 
 
It works this way: You study, pray, listen to the spirit and act. 
 
If baptism feels right, you move ahead. If not, but you want to continue to study, then, that's what you do. You decide if their message is not for you.  
 
Be sincere, be serious, and ask in faith. 
 
If you do study with missionaries, you may find their excitement and enthusiasm for your opportunity to drive them rapidly, and that's ok, they are sincere in their desire for you to receive blessings, but you are in control of your own conversion.