We demonstrate that growth rate bistability for bacterial cells growing exponentially at a fixed external antibiotic concentration can emerge when the cell wall permeability for the drug is low and the growth rate sensitivity to the intracellular drug concentration is high. Under such conditions, an initially high growth rate can remain high, due to dilution of the intracellular drug concentration by rapid cell volume increase, while an initially low growth rate can remain low, due to slow cell volume increase and insignificant drug dilution. Our findings have implications for the testing of novel antibiotics on growing bacterial strains.