I have a Bike Friday. It will fit into a suit case, but you have to take things apart, more than just folding it up.
If you have problem with taking things apart, (really it is a bigger problem putting it back together) you could have a bike shop do the work.
With the Friday, the entire bike and wheels (bike and trailer. The suit case becomes a trailer with attaches to the bike easily) fit into the suit case. You have to put your panniers in a separate bag.
If you fly yourself, take the rear seats out of the airplane, remove the wheels, wrap an old towel around the chain, sprockets, etc., remove the seat, disconnect the brake and gear shifting cables from the top tube and then rotate the handle bars 180 degrees.
Then place the bike into the airplane upside down, with the handle bars in the back.
Works perfect for me.