In the field of WiFi sensing, as an alternative sensing source of the channel state information (CSI) matrix, the use of a beamforming feedback matrix (BFM)that is a right singular matrix of the CSI matrix has attracted significant interest owing to its wide availability regarding the underlying WiFi systems. In the IEEE 802.11ac/ax standard, the station (STA) transmits a BFM to an access point (AP), which uses the BFM for precoded multiple-input and multiple-output communications. In addition, in the same way, the AP transmits a BFM to the STA, and the STA uses the received BFM. Regarding BFM-based sensing, extensive real-world experiments were conducted as part of this study, and two key insights were reported: Firstly, this report identified a potential issue related to accuracy in existing uni-directional BFM-based sensing frameworks that leverage only BFMs transmitted for the AP or STA. Such uni-directionality introduces accuracy concerns when there is a sensing capability gap between the uni-directional BFMs for the AP and STA. Thus, this report experimentally evaluates the sensing ability disparity between the uni-directional BFMs, and shows that the BFMs transmitted for an AP achieve higher sensing accuracy compared to the BFMs transmitted from the STA when the sensing target values are estimated depending on the angle of departure of the AP. Secondly, to complement the sensing gap, this paper proposes a bi-directional sensing framework, which simultaneously leverages the BFMs transmitted from the AP and STA. The experimental evaluations reveal that bi-directional sensing achieves higher accuracy than uni-directional sensing in terms of the human localization task.