Will AirDrop use the data allowance from my phone and wifi modem?

I'm successfully able to transfer files from my iPhone to my MacBook Pro using AirDrop, when connected to my home wifi network. But I'm unable to determine how AirDrop is creating the connection between the phone and laptop.

This page says:

AirDrop uses Apple's Bonjour technology to listen in on a wireless connection for another Mac to announce AirDrop capabilities

and this page says:

AirDrop uses Bluetooth to create a peer-to-peer Wi-Fi network between the devices.

When my laptop is connected to a wifi modem, and my phone is using 4G data, will AirDrop use the wifi and 4G connections, eroding my data allowances on both devices? Or are the phone and laptop directly connected to each other ("peer to peer wireless network"), and therefore not eating up my data allowances?

With airdrop it is always a direct connection (usually wifi or a mix of wifi + bluetooth) between the 2 devices. No internet connection is required at all. So you can transfer as much as you like and it will all be local between the devices; "peer to peer" like you say. Your internet quota won't be used at all.