They should be tight enough to not turn, and when tight, you should be able to "pinch" it together a little bit, and I do mean a little bit, by taking your hand and tightening against it.
Head bumpers work well, but some horses will be aggravated by them, some won't.
How far are you going, and in what weather?
We've shipped with them and without them. Just depends on your horse really, and even if put on correctly at the optimum tightness? Still doesn't mean your horse won't get one off.
Horses make me a better person.