Q: What day of the month does Apple bill your bank account for Apple Music?

Hi,

If you started your Apple Music membership today, then subsequent charges would be on or about the same time of the month for the duration of the membership.

"your account is billed at the time of or shortly after your transaction."

Above quote from this support article >  How iTunes Store purchases are billed

When you first join Apple Music, you get one free, three-month trial membership per person or family. To join, you need to enter a valid payment method, but you will be billed for your membership only after the trial period ends.