RNA aptamers are relatively short nucleic acid sequences that bind targets with high affinity, and when combined with a riboswitch that initiates translation of a fluorescent reporter protein, can be used as a biosensor for chemical detection in various types of media. These processes span target binding at the molecular scale to fluorescence detection at the macroscale, which involves a number of intermediate rate-limiting physical (e.g., molecular conformation change) and biochemical changes (e.g., reaction velocity), which together complicate assay design. Here we describe a mathematical model developed to aid environmental detection of hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) using the DsRed fluorescent reporter protein, but is general enough to potentially predict fluorescence from a broad range of water-soluble chemicals given the values of just a few kinetic rate constants as input. If we expose a riboswitch test population of Escherichia coli bacteria to a chemical dissolved in media, then the model predicts an empirically distinct, power-law relationship between the exposure concentration and the elapsed time of exposure. This relationship can be used to deduce an exposure time that meets or exceeds the optical threshold of a fluorescence detection device and inform new biosensor designs.