The kinds of human activities occupants are engaged in within indoor spaces significantly contribute to the spread of airborne diseases through emitting aerosol particles. Today, ubiquitous computing technologies can inform users of common atmosphere pollutants for indoor air quality. However, they remain uninformed of the rate of aerosol generated directly from human respiratory activities, a fundamental parameter impacting the risk of airborne transmission. In this paper, we present AeroSense, a novel privacy-preserving approach using audio sensing to accurately predict the rate of aerosol generated from detecting the kinds of human respiratory activities and determining the loudness of these activities. Our system adopts a privacy-first as a key design choice; thus, it only extracts audio features that cannot be reconstructed into human audible signals using two omnidirectional microphone arrays. We employ a combination of binary classifiers using the Random Forest algorithm to detect simultaneous occurrences of activities with an average recall of 85%. It determines the level of all detected activities by estimating the distance between the microphone and the activity source. This level estimation technique yields an average of 7.74% errors. Additionally, we develop a mask detection classifier to determine if an active source uses a mask with a recall score of 75%. All these intermediary outputs make critical predictors for AeroSense to estimate the amounts of aerosol generated from the active human source. Our model to predict aerosol is a Random Forest regression model, which yields 2.34 MSE and 0.73 r-squared value. We demonstrate the accuracy of AeroSense by validating our results in a cleanroom setup and using advanced microbiological technology. We present results on the efficacy of AeroSense in natural settings through controlled and in-the-wild experiments. The ability to estimate aerosol emissions from detected human activities is part of a more extensive indoor air system integration, which can capture the rate of aerosol dissipation and inform users of airborne transmission risks in real-time.