Understanding the holistic city-wide impact of planned transportation solutions and interventions is critical for decision making, but challenged by the complexity of the urban systems, as well as the quality of the available urban data. The cornerstone for such impact assessments is estimating the transportation mode-shift resulting from the intervention. Although transportation planning has well-established models for the mode-choice assessment such as a nested multinomial logit model, an individual choice simulation could be better suited for addressing the mode-shift allowing us to consistently account for individual preferences. Moreover, the available ground-truth data on the actual transportation choices is often incomplete or inconsistent. The present paper addresses those challenges by offering an individual mode-choice and mode-shift simulation model and the Bayesian inference framework, and demonstrates how impact assessments can be performed in the events of incomplete mobility data. It accounts for uncertainties in the data as well as the model estimate and translates them into uncertainties of the resulting mode-shift and the impacts. The framework is evaluated on the two intervention cases: introducing ride-sharing for-hire-vehicles in NYC as well the recent introduction of the Manhattan Congestion surcharge. It can be used to assess mode-shift and quantify the resulting economic, social and environmental implications for any urban transportation solutions and policies considered by decision-makers or transportation companies.