<p>The replacement of traditional aggregates with recycled rubber in concrete is increasingly attractive, driven by sustainability-related considerations. Nevertheless, incorporating rubber particles alters both the microinterfacial characteristics and the macroscopic performance of concrete, which leads to the variation in bond behavior between rebar and rubberized concrete. Against this background, 42 central pull-out specimens were prepared for bond tests, and the impact of the rubber replacement ratio (<i>ρ</i>_rv) on the bond behavior was investigated. Moreover, specimens with different confined conditions were designed to identify a reliable strengthening scheme for crumb rubber concrete (CRC) members. The test results show that when <i>ρ</i>_rv increases from 0% to 30%, the crack width of the splitting specimens decreases, but the bond strength deteriorates simultaneously. When <i>ρ</i>_rv increases to 40%, the specimens are subjected to pull-out failure, and the deterioration of the bond strength can be alleviated. Specimens strengthened by fiber-reinforced polymer (FRP) and/or stirrups undergo pull-out failure and exhibit higher bond strength than that of their unstrengthened counterparts. Confinement enhances the bond strength of CRC specimens, beyond which further confinement induces no additional gains. By calibrating rubber-influenced parameters and the confinement critical effect, a mechanics-based model is established for predicting the bond strength of the CRC–rebar interface. Finally, the stochasticity of the bond–slip response is simulated based on the assumption of multi-composite spring–friction units fracturing stochastically, and a continuous bond–slip model with high accuracy and an integral absolute error (<i>E</i>_IA) below 10.47% is proposed.</p>