How to reference taxonomy used by other content type?
For simple displaying of taxonomy term

Assuming your are using entityreference for Drupal 7 the module provides out of the box a field formatter that allows you to display the Rendered entity with a specific view mode 

Thus you can display the referenced entity with the taxonomy term included.

Go to the manage display of your Content B and change the format to Rendered entity and choose teaser for the view mode

 

Go to the manage display of your Content A and modify the teaser view mode and add the taxonomy term field to be displayed.

For more advanced use cases

You might want to try any combination of the following 


field_extractor to extract a specific field from a referenced entity
inline_entity_display similar to above
field_reference refer to specific field on the same node/entity or other node/entities