In this paper, we investigate the problem of joint direction of departure (DoD) and direction of arrival (DoA) estimation with bistatic MIMO radar. Specifically, a weaved co-prime array (WCA) bistatic MIMO (WCA-bMIMO) radar is proposed to produce a hole-free sum-difference co-array, which enables to offer significantly increased degrees of freedom (DoFs) and enlarged array aperture. Moreover, the two-dimensional spatial smoothing method is introduced to construct a smoothed received signal, which helps to tackle the rank deduction problem rooted in the equivalent one-snapshot received signal from the sum-difference co-array. Subsequently, the joint DoD and DoA estimates can be obtained by extracting the three-way tensor model. Furthermore, co-array Cramer-Rao Bound (CRB) for the bistatic co-prime MIMO radar is provided. Finally, the superiorities of the proposed bistatic co-prime MIMO radar in accuracy and resolution are proved by numerical simulation results.