Generally, bluetooth is allowed, especially US airlines. Air Canada is an exception. The last time I flew them, they explicitly stated that bluetooth devices, including headphones, are not allowed at any time during the flight.
Agree that if you want cheaper wired, Bose QC25 are a good choice. Some of the Audio-Technica are also good, but QC25 are better. There are also some bluetooth adapters for them which look and work well, although I've typically seen them more in the $60-70 range. \
Can't comment on the Sennheiser HD4.05 with ANC. Looks like a nice set and gets some solid reviews.