Monocular visual inertial odometry (VIO) has facilitated a wide range of real-time motion tracking applications, thanks to the small size of the sensor suite and low power consumption. To successfully bootstrap VIO algorithms, the initialization module is extremely important. Most initialization methods rely on the reconstruction of 3D visual point clouds. These methods suffer from high computational cost as state vector contains both motion states and 3D feature points. To address this issue, some researchers recently proposed a structureless initialization method, which can solve the initial state without recovering 3D structure. However, this method potentially compromises performance due to the decoupled estimation of rotation and translation, as well as linear constraints. To improve its accuracy, we propose novel structureless visual-inertial bundle adjustment to further refine previous structureless solution. Extensive experiments on real-world datasets show our method significantly improves the VIO initialization accuracy, while maintaining real-time performance.