VRay GPU is only compatible with the texmaps that Chaos explicitly enables for it, which is why tyBitmap is not compatible.
So you have 2 options: 1) you can render with VRay CPU, or 2) you can manually create a multi-sub material where each sub material holds a single frame of animation, then you can have particles' material ID override change over time to match the frame/framerate you want to play back on the particles. Ultimately you'd probably want to create that setup (the multi-sub material holding all the frames) with MAXScript, or else it would be a very tedious process to set up manually. So, for example, if you have 100 frame animation, you'd create a multi-sub material with 100 sub-materials, each holding a single frame of your animation in sequence...then each particle's material ID override would need to be synced to whichever frame you want to display from the animation on each particle, over time. That's basically what tyBitmap does internally.
So you have 2 options: 1) you can render with VRay CPU, or 2) you can manually create a multi-sub material where each sub material holds a single frame of animation, then you can have particles' material ID override change over time to match the frame/framerate you want to play back on the particles. Ultimately you'd probably want to create that setup (the multi-sub material holding all the frames) with MAXScript, or else it would be a very tedious process to set up manually. So, for example, if you have 100 frame animation, you'd create a multi-sub material with 100 sub-materials, each holding a single frame of your animation in sequence...then each particle's material ID override would need to be synced to whichever frame you want to display from the animation on each particle, over time. That's basically what tyBitmap does internally.