Yes, you want the wood to dry out the sides, not out the ends which will cause cracking and splitting.
I harvest many types of woods for bow making (by the ton). When I get the wood home, I paint the ends with wood glue (lots of sealants will work), and store the wood in a dry protected area. Keep the bark on until ready for use! The bark will let the wood dry out slower and, some types of bark keep wood eating bugs away.
I use a moisture meter on seasoned staves that helps me determine if the stave is too wet or too dry for bow making. Some of my osage staves I can use within a 2-year period from cutting. Others, I will wait 5-years (or more) before considering the wood. Just depends on what type of bow I will be making with it.
BTW, it is not necessary to follow one grain on the bow back if the bow is going to be backed with sinew or rawhide. I have made dozens and dozens of bows using both methods and can't tell the difference. If the bow is not going to be backed, by all means, follow one grain completely through the construction or during the expansion of the back (while shooting) that violated grain will raise resulting in a broken bow.