Smartphone sensors allow measurement of phenomena that are difficult or impossible to capture via self-report (e.g., geographical movement, physical activity). Sensors can reduce respondent burden by eliminating survey questions and improve measurement accuracy by replacing/augmenting self-reports. However, if respondents who are not willing to collect sensor data differ on critical attributes from those who are, the results can be biased. Research on the mechanisms of willingness to collect sensor data mostly comes from (nonprobability) online panels and is hypothetical (i.e., asks participants about the likelihood of participation in a sensor-based study). In a cross-sectional general population randomized experiment, we investigate how features of the request and respondent characteristics influence willingness to share (WTS) and actually sharing smartphone-sensor data. We manipulate the request to either mention or not mention (1) how participation will benefit the participant, (2) participants' autonomy over data collection, and (3) that data will be kept confidential. We assess nonparticipation bias using the administrative records. WTS and actually sharing varies by sensor task, participants' autonomy over data sharing, their smartphone skills, level of privacy concerns, and attitudes toward surveys. Fewer people agree to share photos and a video than geolocation, but all who agreed to share photos or a video actually did. Some nonresponse and nonparticipation biases are substantial and make each other worse, but others jointly reduce the overall bias. Our findings suggest that sensor-data-sharing decisions depend on sample members' situation when asked to share and the nature of the sensor task rather than the sensor type.