Never ever iron your garment bag if you want to preserve its elasticity and nature. As mentioned, a majority of these bags are made from Nylon, Polyester, or Leather. It is clear that leather should not be ironed and nor should the other named fabrics. Nylon and Polyester are not made to withstand high heat and can literally melt if ironed.
Luckily, these items are made to keep your clothes on the inside without wrinkles, therefore the shell of these bags are not prone to wrinkles themselves.