Accurate extraction of natural frequencies of the Polyester Filament Yarn (PFY) vibration can effectively estimate PFY tension. However, due to the special working operating conditions of spinning equipment, the collected PFY vibration signals always contain strong noise components, which severely affect the analysis and processing of those signals. Stochastic resonance has received extensive attention and research in enhancing and extracting feature signals. In this paper, a time-delayed feedback bistable stochastic resonance (TFBSR) system is proposed and the feasibility of the system for natural frequencies extraction is discussed. The potential function, the probability density, the mean first-passage time and the SNR-theory are used to evaluate the TFBSR system. Firstly, through adaptive tuning parameters including barrier parameters, feedback strength, time delay and noise intensity in the TFBSR system, the weak PFY vibration signal, the noise, and the potential can be matched with each other to an extreme, and an optimal output with low-noise interference can be obtained consequently. Secondly, numerical simulation results show that the noise intensity has played an active role in the stochastic resonance effect. Finally, the combination of the TFBSR system and the improved wavelet threshold denoising model is conducive to extracting the natural frequencies of the PFY and making the estimation of the PFY tension in the spinning process. The experimental results indicate that the TFBSR system can accurately extract the natural frequency and improve the energy of the PFY vibration signal under the appropriate system parameters.