How do I display fields in my product type in a product display?
Fields from the referenced product entity are automatically available on the product display node.

Set the fields to visible on the product at

admin/commerce/products/types/subscription-product/display

Then, set the fields to display at:

admin/structure/types/manage/product-display/display

Update: As noted by vintorg below when creating your product reference field on the product display node, ensure "Render fields from the referenced products when viewing this entity." is checked.

That should do it.