Because the development of the internet of things (IoT) requires technology that transfers information between objects without human intervention, the core of IoT security will be secure authentication between devices or between devices and servers. Software-based authentication may be a security vulnerability in IoT, but hardware-based security technology can provide a strong security environment. A physical unclonable functions (PUFs) are a hardware security element suitable for lightweight applications. PUFs can generate challenge-response pairs(CRPs) that cannot be controlled or predicted by utilizing inherent physical variations that occur in the manufacturing process. In particular, pulse width memristive PUF (PWM-PUF) improves security performance by applying different write pulse widths and bank structures. Bloom filter (BF) is probabilistic data structures that answer membership queries using small memories. Bloom filter can improve search performance and reduce memory usage and are used in areas such as networking, security, big data, and IoT. In this paper, we propose a structure that applies Bloom filters based on the PWM-PUF to reduce PUF data transmission errors. The proposed structure uses two different Bloom filter types that store different information and that are located in front of and behind the PWM-PUF, improving security by removing challenges from attacker access. Simulation results show that the proposed structure decreases the data transmission error rate and reuse rate as the Bloom filter size increases, the simulation results also show that the proposed structure improves PWM-PUF security with a very small Bloom filter memory.