The string doesn't have to run down the center of the handle nor do the limbs have look the same. Is it in the handle at all? I have made bows where the only place the string is over wood is one point in the handle. In a crooked bow like that I always wait to choose upper and lower limb until I see where the string goes. Then I select the limb that makes the bow the most center shot. If you have to bend it, stay away from places the limb was bent before. If the tips were recurved with heat, heating again there can cause the tip to return to it's former shape unless you have it clamped in a caul. I've had decent luck bending bows in the handle as John suggested. It takes a lot of heat though. A heat gun is the way to go. Light bulbs will never be enough.
George