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• Cyclists were clustered based on socioeconomic strata, gender, education and vehicle access. • Potential accessibility distance decay functions are used to assess equality indices. • 90% of women who cycle have access to 30% of the opportunities in a monocentric city. • In cities from the Global South the bicycle is positioned as a potential vehicle to redress social inequalities. • Understanding the concept of accessibility applied to the bicycle is a powerful resource for decision-makers. In a context of rising awareness for environmental concerns and promotion policies targeting non-motorized travel as a sustainable mobility solution, the bicycle has increasingly become an attractive transport mode in cities. However, accessibility to opportunities for people who cycle is not necessarily the same across socioeconomically different population segments, and it tends to be further constrained by high costs associated with the travel distance through the road network. This research examines equality in the accessibility to employment and education among cycle-user adults in Bogotá. Using 968 reported bicycle trips with these travel purposes in the 2015 Bogotá Household Travel Survey, we estimate a potential accessibility indicator and horizontal and vertical equality indicators. First, we identify three clusters through the K-prototypes method to classify bicycle commuters based on trip and socioeconomic characteristics, and second, we calculate potential accessibility using GIS-based trip distance decay functions, which is later assessed through equality indices such as Lorenz Curves, Gini index and Palma Ratio. Results show marked differences in potential accessibility to work and study opportunities between and within clusters, where up to 90% of the analyzed population of a cyclists' cluster has access to 30% of the job and study opportunities, indicating social and spatial inequalities produced by the urban structure and individual and household characteristics of regular cyclists. Results can guide in the implementation of accurate transport policies towards more equitable and sustainable transport in cities that are experiencing increases in bicycle ridership. [ABSTRACT FROM AUTHOR]