From lclev over at: http://www.mac-forums.com/macos-operating-system/317780-airdrop-discovered-optio ns.html
Okay reporting back. I did some research and according to Apple, air drop will not work between an iOS 8 device and a laptop earlier than 2012 even if it is running OS X 10.
In order to transfer files between a Mac and and an iPhone, iPad or iPod touch, your iOS device needs iOS 7 or later installed and your Mac needs to be a 2012 or later model.
You can transfer files between two Mac computers but you need one of the Mac models listed below and OS X Lion or later.
MacBook Pro (Late 2008 or newer)*
MacBook Air (Late 2010 or newer)
MacBook (Late 2008 or newer)*
iMac (Early 2009 or newer)
Mac Mini (Mid 2010 or newer)
Mac Pro (Early 2009 with AirPort Extreme card, or Mid 2010)
*The MacBook Pro (17-Inch Late 2008) and the white MacBook (Late 2008) do not support AirDrop.
bonds1972 - I did try it on my MB Pro early 2011 and I had the same screen you had show up when the only devices were iOS devices. When I tried it between my MB Pro 2011 and MB Air 2013 it worked but the 2011 took a while to see the 2013. I don't see this as being a good way to transfer files for the 2011.
Lisa
Update - I need to clarify what happens with air drop on an older computer.
In order to use it both have to have Finder open. AirDrop has to be selected on both. On my 2013 MB Air I have to select at the bottom "Don't see what your looking for?" A drop box appears with the selection" Search for an Older Mac" When I click on that they "see" each other. I open a second Finder window on both so I can drag and drop files. The files appear in my downloads folder.
Lisa