Bulk bitwise operations, i.e., bitwise operations on large bit vectors, are prevalent in a wide range of important application domains, including databases, graph processing, genome analysis, cryptography, and hyper-dimensional computing. In conventional systems, the performance and energy efficiency of bulk bitwise operations are bottlenecked by data movement between the compute units and the memory hierarchy. In-flash processing (i.e., processing data inside NAND flash chips) has a high potential to accelerate bulk bitwise operations by fundamentally reducing data movement through the entire memory hierarchy. We identify two key limitations of the state-of-the-art in-flash processing technique for bulk bitwise operations; (i) it falls short of maximally exploiting the bit-level parallelism of bulk bitwise operations; (ii) it is unreliable because it does not consider the highly error-prone nature of NAND flash memory. We propose Flash-Cosmos (Flash Computation with One-Shot Multi-Operand Sensing), a new in-flash processing technique that significantly increases the performance and energy efficiency of bulk bitwise operations while providing high reliability. Flash-Cosmos introduces two key mechanisms that can be easily supported in modern NAND flash chips: (i) Multi-Wordline Sensing (MWS), which enables bulk bitwise operations on a large number of operands with a single sensing operation, and (ii) Enhanced SLC-mode Programming (ESP), which enables reliable computation inside NAND flash memory. We demonstrate the feasibility of performing bulk bitwise operations with high reliability in Flash-Cosmos by testing 160 real 3D NAND flash chips. Our evaluation shows that Flash-Cosmos improves average performance and energy efficiency by 3.5x/32x and 3.3x/95x, respectively, over the state-of-the-art in-flash/outside-storage processing techniques across three real-world applications.