I had the same problem and figured out.
My case was: airdrop wouldn't connect mi new iPhone 5s with my old iPhone 5.
I Tried all possible combinations of settings: on/off Bluetooth, wifi, airdrop, for everyone/contacts only, disconnected from wifi. Nothing worked. The point is i had my new iPhone 5s with the personal hotspot on, and the iPhone 5 was previously connected there. Even when i disconnected the iPhone 5 of the personal hotspot of iPhone 5s it wouldn't work.
So what i did was: i turned off hotspot on iPhone 5s, disconnected both phones of wifi, turned off airdrop, wifi and Bluetooth on both phones, and turned off, then on both phones. When they rebooted, i turned on airdrop for everyone in both phones, immediately wifi and Bluetooth started, i shared a picture and " taraaaa" it worked!