If they did not like/accept my quote, I just had them pay me what they thought it was worth. If it was too low, I would thank them and decline to come back and mow for them again. Sometimes they paid me what I asked, but they declined to have me come back as they thought it was too much.
Usually the first time took way longer than subsequent visits, as it often had gone awhile without being mowed. So I think they weighed my quote against time taken in deciding if it was a good deal.
It was a hassle getting all the when school was in session; I grew up in CA so long growing season. But my 10-15 hours of work per week, I would make more than someone working full time at minimum wage.