Does AirDrop use up Bandwidth?
AirDrop creates a direct connection to another Mac through it's wireless card and therefor does not transfer across your LANs wired network or wireless network and most certainly does not effect your internet bandwidth.
Here are 4 possible reasons for the high bandwidth.
You are unaware of software on your Mac because someone else has installed it on your behalf. Perhaps Online Backup Software or you may have installed it yourself and not been aware of the repercussions. i.e. Crashplan/Dropbox etc.
Your network has been compromised by a Neighbour via wireless. Reset your wireless routers password and make sure it is set to use a secure protocol i.e. WPA2
You have another device on your network to do with streaming Movies to your TV like Netflix.
You have signed up for iTunes Match and have synced Music and Movies to all your Mac devices.
AirDrop sets up a direct connection between two computers on the local network, so it won't send anything over the internet. You might need to look elsewhere for the usage.