Coal and rock burst are one of the main dynamic disasters that affect coal mine production. In this paper, the burst structural model of the rock-coal-bolt (RCB) system and the burst tendency criterion are established on the background of deep thin coal seam mining. Uniaxial and triaxial mechanical tests under different stress states are carried out on RCB specimens with different angles. Combined with thermal imaging, the mechanical behavior of the inclined RCB specimen under uniaxial loading is discussed. The results show that the burst tendency of the RCB specimen increases with the angle. The stress-strain curves of some uniaxial and triaxial test specimens show two or more peaks, and the thermal imaging evolutionary process shows that the cracks of the coal and rock develop from shear to tension shear cracks. There is a further development of fracture and energy accumulation between the first and second peaks in the stress-strain curve of the specimen. Therefore, the failure degree of the second peak of the specimen may be stronger than that of the first peak. Additionally, the established stiffness coefficient and burst energy index can better describe the burst tendency of the RCB specimen under different stress states. The results show that the burst tendency of the RCB specimen under the triaxial test is much higher than that of the uniaxial test. In other words, it also explains that the essence of the burst failure of the surrounding rock in the roadway is the initial instability induced by the inside surrounding rock in the roadway. Moreover, the burst tendency is the largest when the rock and coal combination angle is 15°, and the burst damage range may also be increased by the failure of internal coal and rock mass.