I am experiencing the same problem.
We have two macs, a 2012 MacBook Pro and a mid-2011 iMac. Airdrop worked fine with both machines using Mavericks.
Since upgrading to Yosemite, Airdrop still works with the MacBook Pro, but not the iMac. In fact, the iMac does not even show the two clickable links at the bottom of the Airdrop Finder window that say "Allow me to be discovered by..." and "Don't see who you're looking for..."
Bluetooth is turned on. We're on the same Wi-Fi network. No Firewall. I created a test admin user account and the problem persists.
Even spoke with Apple tech and they couldn't help.
Any suggestions?