Abstract: To reveal the influences of bedding dip angle and anchorage type on the failure mechanism and instability precursor characteristics of coal-rock composite specimens, uniaxial compression tests were carried out on coal-rock combinations with bedding dip angles of 15°, 30° and 45° under unreinforced, PR bolt-reinforced and NPR bolt-reinforced conditions. Acoustic emission (AE) instruments and CCD cameras were used to monitor the failure mode, peak strength and evolution characteristics of AE energy rate of the composite specimens. Based on the critical slowing-down theory, two characteristic indicators, i.e., weighted fluctuation asymmetry and mean absolute deviation, were innovatively proposed. The occurrence sequence of precursor indicators was clarified, and the influences of bedding dip angle and different anchorage conditions on the critical slowing-down characteristics and early-warning timing were investigated. Within the investigated range of 15°–45°, increasing the interface inclination changes the failure mode of coal-rock composite specimens from tensile-shear composite failure toward shear-dominated failure, accompanied by increased failure severity, higher peak AE energy rate, and a reduced relative restraining effect of the bolts. At the same bedding dip angle, the NPR bolt-reinforced specimens exhibit the lowest failure degree and the highest peak strength. The peak AE energy rate of NPR bolt-reinforced specimens is reduced by 62.50%–83.34% and 27.28%–46.22% compared with unreinforced and PR bolt-reinforced specimens, respectively. The AE energy critical slowing-down precursors of PR and NPR bolt-reinforced specimens present the same evolution law, with the sequence of weighted fluctuation asymmetry > recovery rate > mean absolute deviation > variance. Within the investigated range of 15°–45°, most precursor-to-failure time ratios generally decreased with increasing interface inclination, and the precursor responses of the 45° specimens appeared relatively earlier. Compared with PR bolts, the weighted fluctuation asymmetry and recovery rate of NPR bolt-reinforced specimens generally exhibited earlier precursor responses under most investigated conditions. The weighted fluctuation asymmetry makes up for the shortcoming that traditional critical slowing-down indicators are difficult to reflect the early instability precursors of the system, and can be used as an effective early-warning parameter to characterize the initial damage of coal-rock composite specimens. The research results clarify the instability precursor evolution law of anchored coal-rock composite system, which provides a theoretical basis for the early warning and prevention of surrounding rock instability disasters in deep complex structural areas with coal-rock interbeds.