The Girl and the Bicycle by Mark Pett

From chapters.ca:
A touching wordless picture book about a little girl, a shiny bicycle, and the meaning of persistence - with an unexpected payoff. A little girl sees a shiny new bicycle in the shop window. She hurries home to see if she has enough money in her piggy bank, but when she comes up short, she knocks on the doors of her neighbors, hoping to do their yard work. They all turn her away except for a kindly old woman. The woman and the girl work through the seasons, side by side. They form a tender friendship. When the weather warms, the girl finally has enough money for the bicycle. She runs back to the store, but the bicycle is gone! What happens next shows the reward of hard work and the true meaning of generosity. Wordless, timeless, and classic, The Girl and the Bicycle carries a message of selflessness and sweet surprises and makes an ideal gift for graduations and other special occasions.