In this paper, we propose a novel active reconfigurable intelligent surface (RIS)-assisted amplitude-domain reflection modulation (ADRM) transmission scheme, termed as ARIS-ADRM. This innovative approach leverages the additional degree of freedom (DoF) provided by the amplitude domain of the active RIS to perform index modulation (IM), thereby enhancing spectral efficiency (SE) without increasing the costs associated with additional radio frequency (RF) chains. Specifically, the ARIS-ADRM scheme transmits information bits through both the modulation symbol and the index of active RIS amplitude allocation patterns (AAPs). To evaluate the performance of the proposed ARIS-ADRM scheme, we provide an achievable rate analysis and derive a closed-form expression for the upper bound on the average bit error probability (ABEP). Furthermore, we formulate an optimization problem to construct the AAP codebook, aiming to minimize the ABEP. Simulation results demonstrate that the proposed scheme significantly improves error performance under the same SE conditions compared to its benchmarks. This improvement is due to its ability to flexibly adapt the transmission rate by fully exploiting the amplitude domain DoF provided by the active RIS.