We consider a scenario in which an operator installs (small cell) base stations on top of city buses to offer better quality of experience (QoE) to their passengers. In that case, providing a consistent backhaul rate (i.e., a constant rate at all times) to these base stations could help mitigate the effects of mobility on the QoE. Specifically, we perform the analysis to determine the maximum consistent backhaul rate that can be offered to a bus on a given route, given the resources allocated by the operator to backhauling, by taking advantage of the fact that different buses on that route will see different conditions at a given time. We also consider the case where we allow a small outage probability, i.e., that the consistent rate is not provided for a small proportion of time. We show that by allowing an outage probability of only 1% we can increase the achievable backhaul rate by 50%. We then show how to compute the Pareto frontier (rate region) of the achievable consistent backhaul rates when there are two bus routes. The analysis is performed under an independence assumption and hence we validate our results by simulations. Altogether, the cost of consistency is very high, but it can be partly mitigated by allocating the unused backhaul capacity to best effort services in real time.