roots coming out of the drain holes does not mean its root bound you wont know that till you pop it out of the pot, but would agree that it is probably due.
if its rootbound the roots will be all balled up along the outside edge of the container and its a good idea to cut the roots a few places along the outside of the ball if its rootbound before repotting. if its not rootbound and it probably isn't you can just transplant into a larger pot without even touching the roots.