Cycling is an important pillar of the global endeavor to have a more sustainable transportation system. Many papers have studied how trip and person characteristics affect selecting the bike as a transport mode but unlike other researchers, we model the probability of cycling using a binary item response model where the choice is modelled as a trade-off between the individuals' tendency to cycle and the threshold related to each cycling situation. We distinguish between frequent and occasional cyclists. The results show that occasional cyclists are more affected by adverse weather situations, darkness, and uphill slopes. Contrary to the previous studies, a separate bike path turned out a stronger motivator for the group of frequent cyclists. The model fit can substantially be improved by accounting for attribute non-attendance. The results show that weather and wind speed have the highest probability to be taken into account, and the bike path had the lowest probability of being considered by the respondents. Employing the attribute non-attendance model made it possible to make accurate and trustworthy conclusions about the attributes by focusing on the people who take into account the attributes. More specifically, it was found that the presence of a separate bike path and a 100% asphalt route can increase the average probability of taking the bike by up to 55 and 40 percentage points, respectively.