Data usage

There's truly no accurate way to answer this. Depending on how you use Apple Music you'll see wildly varying results. If you stream your music versus downloading it to your devices via Wi-Fi, you're gonna use a lot more data. If you listen to Radio in Apple Music or watch music videos on cellular, you're gonna consume more data.

Any music not physically on your device will require data. i.e an internet connection to get to it. If you make it available offline prior to going out of wifi range, then it won't use data.

Listening 2 hours a day with an average 6MB per 3 minute song. About 240MB a day, times 30 days a month is somewhere in the neighborhood of 7GB a month just from music alone. You'll need to add browsing and other internet usage from apps and services to that. This is a very wide average however.

If you stream Apple Music while your iOS device is connected to cellular you're going to consume data. As indicated by the above calculations that usage can be significant. Having said that you can use Apple Music without using a lot of carrier data.

I stream Apple Music while at home and when connected via wifi at the office and other locations with wifi access. For usage in the car, on the bus, and so on I've created several offline listening playlists. I download all of the tracks on those playlists and only listen to local (on device) music when I'm not on wifi. Using this method I consume almost no cellular data using Apple Music.

You can also check with your wireless provider and see if they have any data plans specifically for streaming music which might reduce your monthly usage.