RFID is widely adopted for tracking and identifying objects, yet conventional tag inventory procedures remain inefficient due to frequent signal collisions and resulting latency. This paper introduces TagMap+, a practical and cost-effective framework leveraging Bloom Filters to significantly accelerate RFID tag detection. TagMap+ eliminates the need for per-tag EPC retrieval by shifting computational hashing to the reader side, using precomputed memory values within commercial off-the-shelf tags. By selectively activating tags through carefully controlled RN16 slot responses, TagMap+ avoids traditional anti-collision mechanisms, achieving rapid and collision-resilient presence detection. The system is implemented on a fully programmable, software-defined RFID reader compatible with the EPCglobal Gen2 protocol. Extensive real-world experiments demonstrate that TagMap+ reduces acquisition overhead by up to 79.53% compared to standard inventory methods, maintains robust compatibility with existing tags, and exhibits reliable performance in dense tag environments. This work represents the first hardware implementation of Bloom Filter-based acquisition in RFID, offering a scalable, efficient, and backward-compatible solution for high-performance RFID deployments.