I had the same issue on a new PC . This is what I have found that works on my computer (Dell
XPS 8930):
1.      Verify that airplay icon visible and functioning
on other PC wired to home network
2.      Run BIG-IP Client in background (this is the VPN I have installed for work); client is running but not connected to VPN
3.      Verify that airplay is working as it is supposed
to on iPhone (play something)
4.      Disconnect PC from local network
5.      Connect back to home network using iPhone
hotspot
6.      Open iTunes on PC (still won’t see airplay);
then close iTunes
7.      Disconnect PC from hotspot and turn off hotspot
8.      Log PC back onto home network
9.      Verify iPhone can still see airplay devices
10.  Reopen iTunes on PC – hopefully airplay icon
will be there; test speaker connection
11.  This whole process may have to be repeated every
time the PC is rebooted for whatever reason
I have no idea why this works but I have found that it works repeatedly. I do NOT have to disable IPV6 as many older posts suggest. If someone out there can explain why this works or have a suggestion how to tweak the system to accomplish the same thing on a permanent basis, I'd love to here it.