Airdrop just doesn't work (brand new hardware)

I've a brand new (2015) MacBook Air and a brand new iPhone 6. They're sat next to each other. Both have wifi and bluetooth turned on, and airdrop is set to "everyone" on the phone. Both use the same Apple ID. When I try and use airdrop, the following problems arise:

1. The MacBook takes about 5 minutes to see the iPhone (i.e. I've got to leave the airdrop window open that long for the phone to show up)
2. The iPhone never sees the MacBook, no matter how long I wait in the sharing menu for it to appear
3. When the phone finally does show up on the MacBook airdrop menu, and I drag a file (jpeg) from the macbook into the phone's icon:
   • the icon says "waiting" for about 2 minutes
   • nothing happens on the phone at all (e.g. no requests to accept files)
   • the macbook eventually says my phone "declined" the file (which of course, I / it didn't)
   • about 2 minutes after that happens, I will sometimes get an error message on the phone saying the transfer failed (this only happens about 25% of the time)

I've had this exact same problem with my iMac and my previous iPhone 5. Is airdrop just fundamentally broken? What happened to "it just works", Apple?