On MacOS there is a way to greatly reduce mDNSResponder's traffic on the local network.
From the manpage for mDNSResponder:
mDNSResponder accepts the following optional arguments:
Append search domains for multi-labeled Partially Qualified Domain Name as well as single-labeled Partially
Qualified Domain Name. This argument is not recommended because of the extra DNS traffic it generates and
its adverse effect on battery life.
Prevent the system from advertising Bonjour services via Multicast DNS.
To cause mDNSResponder to run with these optional arguments when it launches on OS X 10.11 (El Capitan) and later, set the
AlwaysAppendSearchDomains or NoMulticastAdvertisements boolean keys to true in /Library/Preferences/com.apple.mDNSResponder.plist and
The second option will stop mDNS from broadcasting bonjour availability, although I don't think it's Bonjour traffic that is your problem, that traffic won't leave the network. I believe you can use a configuration profile to duplicate this on iOS.
Because of recent security news, most of it bad, you might want to take some time to make sure that some apps are not ferrying screenshots of your screen, or, in my case, slyly pumping out half a gig in the dead of the night.
I found turning off bluetooth at night stopped this.