This paper investigates the spectrum hole utilization of cooperative schemes for the two-way relaying model in order to improve the utilization efficiency of limited spectrum holes in cognitive radio networks with imperfect spectrum sensing. We propose two specific bidirectional secondary data transmission (BSDT) schemes with two-step and three-step two-way relaying models, i.e., two-BSDT and three-BSDT schemes, where the spectrum sensing and the secondary data transmission are jointly designed. In the proposed cooperative schemes, the best two-way relay channel between two secondary users is selected from a group of secondary users serving as cognitive relays and assists the bi-directional communication between the two secondary users without a direct link. The closed-form asymptotic expressions for outage probabilities of the two schemes are derived with a primary user protection constraint over Rayleigh fading channels. Based on the derived outage probabilities, the spectrum hole utilization is calculated to evaluate the percentage of spectrum holes used by the two secondary users for their successful information exchange without channel outage. Numerical results show that the spectrum hole utilization depends on the spectrum sensing overhead and the channel gain from a primary user to secondary users. Additionally, we compare the spectrum hole utilization of the two schemes as the varying of secondary signal to noise ratio, the number of cognitive relays, and symmetric and asymmetric channels.