You don't need bold chocobos, I just recently did it with one timid and one normal chocobo in the fray. And also, you can send them where ever you want, it doesn't have to be just the Calm Lands. Bold chocobos like going to the Calm Lands, but it's not necessary.

A problem that a lot of people have is that when they have their level 5 chocobos come back safely, they expect the scene to just happen. You have to exit and reenter the Chocobo Ranch after your level 5 chocobos come back safely, and then the scene will happen. So make sure of the following:

1. You've sent out 3 or every level of chocobo and they've all come back safely.
2. You have four level 5 chocobo runners.

That's all you need to do, the type of chocobo you send out or where you send them doesn't matter. If you've done all this, and you exit and reenter the Chocobo Ranch, then the scene will happen. If it doesn't, then you've missed something.