Phase transitions of single-walled boron nitride nanotube bundles under high pressure were investigated. Multiple three-dimensional boron nitride allotropes were identified from the transition products, which highly depended on factors including compressing mode, nanotube geometry, and intertube orientation. Sequential theoretical calculations indicated a variety of electronic and mechanical properties for these novel boron nitride polymorphs, such as tunable bandgap, ductility, high tensile strength, and superhardness. Especially, a direct bandgap superhard phase, 3D (10,0)-III, and a ductile superhard phase, 3D (4,4)-I, were revealed. This study should stimulate further theoretical and experimental works on novel boron nitride allotropes with unique electronic and mechanical properties.