I usually send my bike to a shop where I am starting the tour. I usually tuck my front panniers in with the bike, along with a few other items, like my seat bag containing tools and tubes
The reassembly charge will usually be about $30. Be sure to contact the bike shop and coordinate with them about the time the bike should arrive there. Be sure you ship your bike off in time.
I check my rear panniers (it might be a good idea to put them in a disposable cardboard box) and carry various items, including my helmet, in a very light backpack which is my carry on, along with my waist pack. On the tour, the backpack holds my clothing inside one of the rear panniers. If I had to, I could wear the backpack for extra capacity.
The airline fees usually charged these days make this procedure about as cheap as flying with the bike, and it is much less hassle.
Check with your carrier (Fedex has a website) for projected shipping times. Allow at least one day for contingencies.