I'm confused by this. Colorspace is metadata, not bit depth. It's a mapping. 8 bit P3 will be exactly the same size was an 8 bit sRGB, except for the additional some hundred bytes of metadata describing the mapping (since missing metadata is assumed sRGB).

For example, you can "convert" an sRGB png to P3 (different colors result, but same bits) by doing nothing but tacking on the icc profile metadata from a P3 image.