From my experiences we always get to the brush before the opponent. I have never encountered an enemy team when we face-checked our brush. The only way they could drive us out would be if they had a pokey team comp
Many teams analyze the level 1 team comp and if they feel they have a disadvantage they won't even get into a position where they could get a fight forced. Without there being any map objectives this early in the game (altars wont spawn until 3:00), they literally lose nothing by not engaging in the "bush behavior".