The value of travel time savings is one of the most widely used concepts in the transportation sector, serving as a critical component of transportation project evaluation, policy formulation, and transportation investment decisions. In this paper, we examine the value of travel time savings as measured using an iterative bidding contingent valuation approach in the context of Mumbai, India. By directly measuring the value of travel time savings, rather than imputing it, we are able to efficiently consider variations across individual characteristics and trip contexts. As importantly, we account for the possibility that some individuals may not be willing to pay at all for travel time savings, jointly modeling a binary outcome representing whether an individual is willing to pay at all (WTP) alongside the continuous value of travel time savings among those who are willing to pay. This approach allows us to identify those individuals who have a value of travel time savings (VTTS) of zero, which may occur due to very different psychological reasons than simply having a low value of travel time savings. The findings reveal significant differences in WTP and VTTS across population subgroups and trip characteristics. The results have important implications for the evaluation of transportation policies, prioritization of transportation infrastructure improvements, and development of priced congestion reduction strategies.