Low expansion foam is the stuff that doesnt get as big after applying. Use the normal stuff, I use it for construction all the time. Trick is to not try and make anything over about 3/4 to 1 inch thick at a time, multiple layers every 12 - 24 hours and the inside wont stay soft and keep expanding.
If you try to fill all behind a urethane bumper in one hit, the inside of the lump will keep expanding and the bumper will get really wavy. Try it first. put a lump on a sheet of newspaper and watch how big it gets. Also put a larger lump and after the outside dries, cut into it and you will see the interior is still soft and curing because it needs air to expand and cure.
Best bet, go slow, little strips at a time and let it COMPLETELY dry between adding layers. A similar product is used in OEM appliactions for stiffening and deadening in A pillars and such in higher end cars such as Audi. Also has been used in channels in flooring to add stiffness (diferent formulas dry extremely hard and inflexable)
good luck and be patient!