Wouldn't the ability to refuse taking the test introduce bias? i.e. the 10% that do take it still may not be representative of the entire population. Likely better than the grocery store sample, but still not ideal
You can also do a separate phone survey in addition to surveying the test participants. Questions like "Do you think you have had COVID?" and "How many times per week do you leave the house?". If the responses for the test participants vary significantly from the phone survey participants, you can try and weight your data accordingly.
There's also literature that suggests that you don't discard outlier values in the actual responders as they may help approximate the non-responder population, i.e., the non-outliers represent typical responders while outliers are more likely to represent non-responders [1]
[0]https://www.warc.com/content/paywall/article/jar/research_no...
[1] https://bmcmedresmethodol.biomedcentral.com/articles/10.1186...