Structural Health Monitoring (SHM) is gaining a key role in ensuring the integrity and safety of civil infrastructures. In the last decades, the rapid shift to wireless sensor networks has given rise to new challenges, mainly related to the limitation of data transmission and payloads, energy autonomy, and computing power needed for extracting useful information. To tackle these issues in the framework of vibration assessment, diverse algorithms have been proposed, mainly inspired by the compressed sensing theory, taking advantage of their inherent sparse nature as a set of multiple exponentially damped sinusoids. However, those solutions usually entail a signal reconstruction step, which is computationally expensive, and demonstrated scarce real-field effectiveness due to significant limitations in the maximum achievable compression ratio. Instead, in this work, we bypass these constraints by proposing an alternative method, termed Bayesian Frequency Identification (BAY-FI), aimed at the identification of the main vibration frequency avoiding the decoding stage. The methodology is wrapped in a Bayesian formulation of an optimized, curve-fitting algorithm applied to random and extremely under-sampled measurement signal. BAY-FI is validated on a laboratory-scale, simply-supported beam and compared with conventional techniques, demonstrating significantly higher compression ratios while taking into consideration the importance of the sensor positioning.