The non-uniform and dynamic nature of Bit-Level Sparsity (BLS) poses a critical load-imbalance challenge for parallel hardware accelerators. While the Bit-Interleaving paradigm, represented by state-of-the-art accelerators like Bitlet, shows promise, it is fundamentally constrained by a rigid datapath and severe inter-channel load imbalance. This paper introduces BitRed, an accelerator that embodies a new ''programmable adaptive bit-interleaving'' philosophy. Rather than a monolithic design, BitRed's core is an Adaptive-Sparse Processing Unit (ASPU) that deconstructs the acceleration process into a set of orthogonal RISC-V ISA extensions for pre-processing (cal.pre), adaptive distillation with dynamic load balancing (cal.adis), and PDP-optimal reduction (cal.red). By transforming a rigid hardware problem into a flexible scheduling problem, this ISA-based approach provides a fundamentally more adaptable and extensible solution. Empirical studies on a broad set of benchmarks highlight the following results (normalized to a SCNN baseline): (1) up to 9.4× speedup over the Bitlet, and 5.6× over the latest bit-serial SOTA BitWave; (2) up to 7.6× higher inference efficiency than Bitlet on representative models; (3) 5.072mm2 area and scalable power consumption from 550.43mW (float32) to 495.12mW (16b) and 457.90mW (8b) @28nm TSMC; and (4) high versatility across precisions, and up to 18.9×13.5× higher than NVIDIA A100 and Jetson Orin 32GB, demonstrating significant competitiveness against GPUs.