Green Book, an Oscar-winning film, tells the story of the journey of a black pianist and his white driver in the southern United States in 1960s. The film depicts the racial discrimination and segregation against blacks in the southern United States at that time, and blacks had to work somewhere every day in exchange for food.
However, this movie is not about getting food by bike. In the movie, Tony, a black pianist, was trapped in a segregated town. He must work somewhere every day in exchange for food. Although cycling may be a common mode of transportation, this film does not describe it in detail.
However, the Green Paper does contain draft contents. Tony was chosen to attend a large concert and had the opportunity to meet the famous black pianist Martin Luther King. This plot may be in line with the situation that you described that the draft changed your fate.
In short, although the film does not directly depict the plot of the protagonist riding a bicycle to get food, it is still a film reflecting racial discrimination and apartheid in the southern United States at that time, and it is worth seeing.