Mobile phone data are increasingly being used to quantify the movements of human populations for a wide range of social, scientific and public health research. However, making population-level inferences using these data is complicated by differential ownership of phones among different demographic groups that may exhibit variable mobility. Here, we quantify the effects of ownership bias on mobility estimates by coupling two data sources from the same country during the same time frame. We analyse mobility patterns from one of the largest mobile phone datasets studied, representing the daily movements of nearly 15 million individuals in Kenya over the course of a year. We couple this analysis with the results from a survey of socioeconomic status, mobile phone ownership and usage patterns across the country, providing regional estimates of population distributions of income, reported airtime expenditure and actual airtime expenditure across the country. We match the two data sources and show that mobility estimates are surprisingly robust to the substantial biases in phone ownership across different geographical and socioeconomic groups.