I came across your query - I am also interested in capturing BPM data for an iPhone app project. Did you have any success in accessing this info? I remember being able to sort my old iTunes library by BPM and extract playlists accordingly, however this may have been via a plugin or separate program which then fed back into iTunes. Apple Music does not seem to hold or surface this information, at least not that I have been able to ascertain - is there any other way of obtaining?