It is bound by the fourth amendment, however you have no inherent right to board a plane. If you want to get on a plane you are voluntarily waiving your right to refuse search. You don't want to give up your right to refuse a search? Don't try to fly.That is a valid criticism of TSA procedures (with which I am naturally familiar.) If you are arguing that TSA procedures are right, then necessarily you are arguing that the Fourth Amendment is wrong. Is the TSA, an agency of the federal government, bound by the Fourth Amendment?
It's also why the courts have historically taken a different view of how automobiles are treated in terms of privacy vs a person's home IIRC.