you should have no real problems cutting and shaping the bow right away.
is it a sapling or a tree to be split?
it can be worked right away but precautions should be taken if you do work on it right away, but by no means will this "ruin" your bow.
if its a sappling work into the desired shape but keep a little lonng, and if it is very close to actual bow dimension really wipe on some grease or renderd fat/lard to keep the moisture loss from escaping too quickly.
if it is rather narrow, you may want to tie it to a 2x4 or something straight for a while to dry a few days.
try to keep way from direct airflow like a fan on top of a wood stove or direct heat for now, try to let it acclimate and loose its moisture closer to the rate at IT wants to.
dont try to force things too much.
things will be ok.
get cutting and working on it so we can see!
bowguy