Feeding acceleration structure to the GPU then raytracing it in a compute shader?
If using the new real-time ray tracing functionality is an option for you, it would be worth a try! It might be that getting it to run is less work than porting your CPU data structure into a GPU-compatible format. Furthermore, using the hardware functionality would result in much better performance since BVH traversal (and triangle intersection, if that is relevant to you) are accelerated in hardware.

Official real-time ray tracing support has been announced by Khronos (in the form of an KHR extension) lately, see Ray Tracing In Vulkan. With the Vulkan API version 1.2, the option for "Ray Queries" has been added. It could be relevant for your use case since it allows to trace rays against the BVH from arbitrary shaders (i.e., e.g., also from compute shaders or fragment shaders).

Using VK_KHR_ray_tracing (or NVIDIA's precursor VK_NV_ray_tracing), you would have to update the acceleration structure on the GPU every time after you have updated your CPU data structure. The API supports updating acceleration structures every frame. In NVIDIA's extension this is done via the VkBool32 update flag in vkCmdBuildAccelerationStructureNV. In the KHR-extension it is handled a bit differently, but in a very similar fashion: The update-flags are contained in the VkAccelerationStructureBuildGeometryInfoKHR structures.