Microbes inhabit natural environments that are remarkably dynamic. Therefore, microbes harbor regulated genetic mechanisms to sense shifts in conditions and induce the appropriate responses. Recent studies suggest that the initial evolution of microbes occupying new niches favors mutations in regulatory pathways. However, it is not clear how this evolution is affected by how quickly conditions change (i.e. dynamics), or which mechanisms are commonly used to implement new regulation. Here, we perform experimental evolution on continuous cultures of Escherichia coli carrying the tetracycline resistance tet operon to identify specific mutations that adapt drug responses to different dynamic regimens of drug administration. We find that cultures evolved under gradually increasing tetracycline concentrations show no mutations in the tet operon, but instead a predominance of fine-tuning mutations increasing the affinity of an alternative efflux pump AcrB to tetracycline. When cultures are instead periodically exposed to large drug doses, all populations evolved transposon insertions in repressor TetR, resulting in loss of regulation and constitutive expression of efflux pump TetA. We use a mathematical model of the dynamics of antibiotic responses to show that sudden exposure to large drug concentrations overwhelm regulated responses, which cannot induce resistance fast enough, resulting in selection for constitutive expression of resistance. These results help explain the frequent loss of regulation of antibiotic resistance by pathogens evolved in clinical environments. Our experiment supports the notion that initial evolution in new ecological niches proceeds largely through regulatory mutations and suggests that transposon insertions are the main mechanism driving this process.