Hi Brandon Sobotta,
Microsoft Band periodically synces to your phone over Bluetooth, typically every half an hour. In addition when you open the Microsoft Health app we perform a sync to ensure you see the most up to date information.
In accordance with Windows Mobile 10's app policies we do not run continuously utilizing CPU or Bandwidth. We do have some background tasks setup, but they are primarily there to kick off the Sync on the half hour boundaries, and also listen for Cortana requests. These are setup as Bluetooth triggers and consume minimal power when not in use.
All in all we do our best to be good mobile citizens!