In order to combat the spread of COVID-19, various measures were taken in most countries to make public transit and paratransit safer. These additional measures, which include restrictions on number of passengers, provision of hand sanitisers and face coverings, and more frequent cleaning, add to the costs of operations or reduce profitability. The resulting financial pressure on the transport operators raises an important question on who pays for these additional measures. In most countries, this has been covered by one-time government bailouts to operators or strategies to increase fare, the latter of which directly affects the users. However, even without these interventions, there could be a demand and as such willingness to pay (WTP) for some of these intervention measures from the consumers concerned about safety. Knowing such WTP will not only help operators set their fare, but also help the governments decide the appropriate bailout needed. This paper addresses the issue by estimating the user's willingness to pay for selected COVID-19 mitigation measures in public transport and paratransit (motorcycle taxis) using survey data collected from two cities in low-income countries as case studies - Kampala, Uganda and Dhaka, Bangladesh. For public transport, these measures are - (1) social distancing (passenger loading at half capacity), and (2) mandatory hand sanitisation and increased cleaning of surfaces, while for paratransit, they are - (1) provision of a transparent shield between the rider and the passenger, and (2) provision of cleaned helmets at the start of each trip. The study analyses stated preference data using the utility maximisation framework and finds that the implementation or provision of COVID-19 mitigation measures improves the attractiveness of the associated public transport or paratransit alternatives, and transport users make trade-offs between safety and cost when making travel decisions. We find positive willingness to pay for all four mitigation measures, suggesting potential existence of a market for these measures. We also find that the typical mode choice factors such as costs, travel time and convenience became less important during the pandemic and the safety measures became more important considerations.