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Public transport travel-time variability (PTTV) is essential for understanding the deteriorations in the reliability of travel time, optimizing transit schedules, and route choices. This paper establishes the key definitions of PTTV which firstly include all buses, and secondly include only a single service from a bus route. The paper then analyzes the day-to-day distribution of public transport travel time by using transit signal priority data. A comprehensive approach, using both parametric bootstrapping Kolmogorov-Smirnov test and Bayesian information criterion technique is developed, recommends lognormal distribution as the best descriptor of bus travel time on urban corridors. The probability density function of lognormal distribution is finally used for calculating probability indicators of PTTV. The findings of this study are useful for both traffic managers and statisticians for planning and analyzing the transit systems.