Your opponent's units can't use Bombard to attack your units in the Ground arena.
Shields 1
Keywords
Bombard
Bombard X: A cumulative, static ability that means, "This unit may attack a unit in the Ground arena instead of the Space arena, using X power plus any other effects." You choose whether to use Bombard to attack a unit in the Ground arena or to make a normal attack in the Space arena. You can't attack a unit in the Space arena using Bombard. Power changes affect Bombard.
Shields
Shields X: A cumulative, static ability that means, "The attacking unit gets –X power against this unit." Shields only matters when attack dice are rolled. If you give a unit Shields after your opponent has rolled for damage, it doesn't affect the roll.