Cotton is unlocked at Level 18.  

Bamboo is unlocked at Level 21. Passionfruit is unlocked at Level 27.

To plant these crops, tap on any bare field. The lower-level crops will appear as usual.

Tap on the ">" (right arrow) at the bottom of the crops for the selection of higher level crops to appear.  

 

Now drag and plant the selected crop as you normally would.