Ballroom Player is a beautiful app that's completely free! Even AD Free!
Apple Music cannot be accessed due to Apple's copyright protection. So, use iTunes to import music into your phone and set your rounds up as you like. Duration, Sequence, break period and tempo... everything you want is built into it!
All bugs are supposedly fixed in this update, but there will always be more discovered in the future =_=
This app is made free for college ballroom dancers but everyone is welcome to download and make good use of it! The competitions are pretty much over this semester, but hopefully it will be helpful to you in the future.
While you're out there(and have a iPhone), check it out.
Go to App Store and Search "Ballroom Player"