In this work, we developed a new Bayesian method for variable selection in function-on-scalar regression (FOSR). Our method uses a hierarchical Bayesian structure and latent variables to enable an adaptive covariate selection in FOSR. Extensive simulation studies show the proposed method's accuracy in estimating the coefficients and high capacity to select variables correctly. Furthermore, we conducted a substantial comparative analysis with the main competing methods, the BGLSS method, the group LASSO, the group MCP, and the group SCAD. Results demonstrate that the proposed methodology is superior in correctly selecting covariates compared with the existing competing methods while maintaining a satisfactory level of goodness of fit. We also considered a COVID-19 dataset from Brazil as an application and obtained satisfactory results. In short, the proposed Bayesian variable selection model is highly competitive, showing significant predictive and selective quality.