Accurate estimation of Expected Time of Arrival (ETA) is an indispensable necessity in modern societies which is intimately intertwined with quality of life for all citizens, especially for commuters and disadvantaged people. In recent years, the widespread adoption of GPS technology has initiated a paradigm shift in ETA estimation. Utilizing GPS data instead of traditional traffic data such as stationary measurements has implications that extend into all technical and methodological aspects of ETA estimation. New technical challenges such as map matching, path inference and travel time allocation arise, and different methodologies, other than well established traffic flow theory, are required. The payoff of such an endeavor, however, is substantial: network-wide coverage of ETA estimation at the fraction of cost compared to traditional approaches. This study is an experimental inquiry into various aspects of developing a fully functional travel time estimation engine, powered solely by public GPS data from bus probe vehicles. Technical hurdles (e.g. map matching, path inference and travel time allocation) are handled in a rather conventional way, with some innovations. The main contribution though, is introduction of computational approach to travel time estimation using Bootstrapped Monte Carlo Simulation. This paves the way for Probabilistic Expected Time of Arrival (P-ETA): an interpretation of travel time in terms of uncertainty, reliability, and variability; instead of merely expected value.</br> Using Bootstrapped Monte Carlo Simulation, a method to derive probability distribution of Route Travel Time (RTT), without prerequisite of intermediate step of estimating probability distribution of Edge Travel Times (ETT), is suggested. The confidence in Travel Time Allocation (TTA) for observations is quantified and used as the weight in unequal bootstrap probability. A number of experiments are carried out to illustrate the ability of the proposed method in identifying spatiotemporal traffic patterns for individual edges, routes, and the network as a whole. It is shown that in addition to travel time, higher order statistics, higher moments of probability distributions and measures of dispersion also exhibit patterns related to spatio-temporal dynamics of traffic, and are likely to be useful as measures of variability and uncertainty of travel time.