The bridge is a pretty difficult map, I'd recommend to go through the free city until you have better equipment. If you cannot get past the fights, it's perfectly fine to just ignore the enemies and just boost past them to reach the next area, which will be an area with friendly NPCs, quests and opportunities to obtain money and better weapons.
At some point you really do need to get used to the fighting though, it won't get much easier even with good body armor etc. It's very frantic and honestly I only manage to kill all enemies on some maps after I learn most of their location by heart.