I'd recommend using mind control from your Avatar on any organic enemies, use these for scouting and early damage. There should be enough cover on your side of the bridge to just set up overwatch and destroy anything that pops into view. Send someone with high movement forward to trigger the avatars and waves of enemies, then run them back. I think that charging in is suicide, you're just asking to get flanked. I'd recommend waiting on the side of the bridge opposite where the avatars and enemies spawn.