How to export paragraph bundles with features?
Paragraphs in D8 are entity types. So to create a feature with a paragraph bundle definition, you will need at least: 


The paragraph type definition 
The Entity form display 
The Entity view display 
The field instances you use.
Core override fields.
Optionally, you will need the field storage definitions.. but generally it is best to put these in a separate feature like core since fields can be used in multiple places.


The easiest way to get all these is to create a new feature and search for paragraph.[type-machine-name].  E.g. I have a paragraph type named banner, so I created a paragraph_banner feature by searching for paragraph.banner and adding the results.