The concept of accessibility has gained considerable attention in the analysis of access to specific facilities for different populations. Unlike motorized systems in which there is no physical limit on the distance that can be traveled, the distance that a given cyclist can travel is variable and is determined by their personal characteristics and the environment. Such maximal travel distance is assumed to delimit the total extension of territory where all the potential interactions of a cyclist may take place and, therefore it affects the accessibility for people who cycle. Despite this variability in the area of influence of each cyclist, accessibility models assume, in the best of cases, a single maximum travel distance, which produces estimates of accessibility that are not very representative of reality. In this article we present more precise estimates of the accessibility of cyclists and compare them with traditional measures. The methodological improvement focuses on two aspects: (1) we calculate variable maximum distances based on the characteristics of the cyclists and the built urban environment. (2) Because the maximum travel distance depends on the characteristics of the built environment, we analyze the impact that the expansion of the dedicated cycling network has on accessibility. Our results reveal that the accessibility patterns depend on the individual characteristics and the built environment. Moreover, our results also confirm that the expansion and densification of the cycling network have an impact on the access to opportunities for cyclists that is not necessarily captured by most classical accessibility measures when considering the variability of cyclists' profiles.