I've never found AirDrop to be reliable. Sometimes it connects, often not. It always takes a long time to make a connection if it does at all
By far the best way to share Notes to all your devices in the Notes app is to link the Notes app to iCloud. I tried resisting Notes in iCloud for a long time, but once you get more than one device - resistance is futile (or foolish). Just do it. If you've got private notes you feel paranoid about, encrypt them with a password.