Bikes are among the healthiest, greenest, and most affordable means of transportation for a better future city, but mobility patterns of riders with different income were rarely studied due to limitation on collecting data. Newly emergent dockless bike-sharing platforms that record detailed information regarding each trip provide us a unique opportunity. Attribute to its better usage flexibility and accessibility, dockless bike-sharing platforms are booming over the past a few years worldwide and reviving the riding fashion in cities. In this work, by exploiting massive riding records in two megacities from a dockless bike-sharing platform, we reveal that individual mobility patterns, including radius of gyration and average travel distance, are similar among users with different income, which indicates that human beings all follow similar physical rules. However, collective mobility patterns, including average range and diversity of visitation, and commuting directions, all exhibit different behaviors and spatial patterns across income categories. Hotspot locations that attract more cycling activities are quite different over groups, and locations where users reside are of a low user ratio for both higher and lower income groups. Lower income groups are inclined to visit less flourishing locations, and commute towards the direction to the city center in both cities, and of a smaller mobility diversity in Beijing but a larger diversity in Shanghai. In addition, differences on mobility patterns among socioeconomic categories are more evident in Beijing than in Shanghai. Our findings would be helpful on designing better promotion strategies for dockless bike-sharing platforms and towards the transition to a more sustainable green transportation.