I understand you are talking about your front bumper, however rear bumpers were a dealer option up until the mid-eighties on many Chevrolet trucks. With regards to the front bumper on your '64, the frame rails and adequately strengthened and aligned by way of the factory cross-members. Unless you have modified or removed some of the factory installed frame rail cross-members, it will not damage the truck in any way to drive with or without the front or rear bumper. Safe and defensive driving is the best way to avoid contact with other moving or fixed objects, thus avoiding the damage caused by such contact.
I suggest a different method for staightening a bent bumper. Secure the bumper to the frame rails with six carriage bolts in the factory holes and bumper brackets. If the ends of the bumper are bent down, simply put a hydraulic jack under the bumper with a block of 2 x 4 or 4 x 4 to protect the finish. Jack until it is a bit past the correct alignment. It will flex back a little, so don't overdue it. You can do the same if it is bent up by reversing the method using the jack and a length of 4 x 4 under the steel support beam in your garage or shop or your overhead door opening.
Good luck with your bumper straightening.
