The emergence of multidrug resistance in Gram-negative pathogens is critically determined by the interplay between efflux pumps activity and low permeation outer membrane. Although phenotypic heterogeneity in isogenic cells is recognized as a key factor of treatment failure, a mathematical framework able to integrate growth dynamics and single-cell heterogeneity in antimicrobial resistance, remains absent. Here we provide such framework that bridges single-cell and colony scales in the context of bacterial survival and efficacy against drugs. Using experimental inputs, our approach produces testable outputs and reveals nontrivial collective effects with key implications for fitness and survival of the colony. This framework provides a mathematical tool to test stress response strategies in organisms that can potentially guide experiments in natural and synthetic cellular systems.