Stand my Ground or Walk??

Two houses down there is a child who goes to pre-school with my daughter. The bus stops at both houses. Since we live on a busy street this sometimes stops up to twenty cars. At first the other child only road the bus home. In the morning the bus stopped at our house and in the afternoon to help keep traffic moving I walked two doors down so both children got off the bus in one stop. This week the child started riding the bus to school as well. On Monday, I suggested to the mother that she walk down to my house is the morning and I'd walk to hers in the PM so we don't hold up traffic (hasn't happened yet).  Yesterday afternoon at the bus stop I asked her what she thought and she said she'd let me know. Today she starting ranting at me via text that she will NOT walk to my house and in fact she believes I should walk to hers both times as her house is the first stop, especially since I'm the one all concerned about traffic. She also tells me that she feels more comfortablee with her daughter being picked up in front of her house. THERE IS ONLY ONE HOUSE BETWEEN US! Not to mention, we are required by law to be out there with them so I am not suggesting her child walk herself to my house. I honestly don't mind walking but then I have to wait with her twice a day and that bugs me. Also, it is scheduled for the bus to stop twice; I was just trying to be helpful. This morning I waited at my house. I can't stand people walking all over me.  Should I walk or stand my ground?