Include View In Node That References Other Nodes Based On Joined Field
Create a View to show nodes of Content Type B, add a Contextual Filter for your field My List and save the view.

Install the Views Field View module and then in the Footer region of your View of Content Type A add the  Global: View (Views field view) and configure under the View settings the Name and Display of your B View and the token for the Contextual filters. 

To use the value of the My List field as a token, you must have in the Fields of your view this field selected.

Edit after your comment ("I'd prefer to keep using the regular node page.")

You can use the EVA module, it provides a Views display plugin that allows the output of a View to be attached to the content of any Drupal entity, in your case the node of Type A. In the contextual filter of the view you need select the My List field in the Entity Content Settings of the View using a token.

"Entity Views Attach: Use Views Almost Anywhere" contains a great tutorial about it.