Time Machine Backup to Airport Time Capsule When I backup using time machine to my Time Capsule, does this use network bandwidth? I'm uncertain as I could see it creating some sort of ad-hoc network between the computer and the disc to do the back up but I'm completely unsure. Just don't want to be backing up hundreds of gigabytes over a network connection
When backing up to a Time Capsule, it backs up over the network.

The first backup will be several hundreds of gigabytes; this takes a while. However, subsequent backups are smaller, since it only transfers files that have changed.

Also, if the Time Capsule is not available (eg MacBook taken offsite), then it creates local snapshots and waits for the Time Capsule to become available again. It won't attempt to transfer the data over your Internet connection.

More info:


HT202301: About Time Machine local snapshots 
HT201250: Mac Basics: Time Machine backs up your Mac