I have a MacBook Air from Mid-2013 and the new iPhone 6S, both running their newest OS (Yosemite and iOS 9).
According to Apple, AirDrop only works on these machines:
Use AirDrop between iOS device and Mac: the iOS device has to be running iOS 8 and has to have a Lightning connector. the Mac needs to be running OS X Yosemite and needs to be a 2012 or newer iMac, 2012 or newer MacBook Air, 2012 or newer MacBook Pro, 2012 or newer Mac Mini or Late 2013 Mac Pro. (Source: 9to5Mac)
So technically it should be compatible, and I also met the necessary other requirements:
Once you have met compatible hardware and software requirements, the devices do have to have Wi-Fi and Bluetooth turned on, even though it works without internet access.
I even put them on the same WiFi network, with working Internet access.
I know that I have the "new" AirDrop on my MacBook Air, since it gives me the option to look for "older Macs". In fact, if I click on that option I can connect to my Late-2009 iMac without a problem, as long as both are on the same WiFi network.
I also tried activating AirDrop "for everyone" on both the MacBook Air and the iPhone but it still didn't work.
Does anyone have an idea why not, or what else I could try out?