Problems with workbench access
To make sure I completely understand your question, I am going to restate it:

User B has created a node from a custom content type and it is assigned to Section One via Workbench Access. User A, who is also assigned to Section One, needs to edit User B's node but is currently unable to. 

You're right in that you need to give people in that role the permission to "Edit Any Content" for that custom Content Type. You can access the permission page at admin/people/permissions, scroll to the "Node" section, find the specific content type in the list and select the proper permissions.

I don't know about what specifically you're trying to develop but I do have a couple of notes for you if it's still applicable to your situation.

First, you might want to consider adding a second role that only has the power to edit content from content types you designate in the permissions page. Using your example, let's say User B is assigned the role of "Author", meaning he can create content and edit/delete his own content. User A is assigned the role of "Editor", meaning she can edit any content User B has created but she cannot create her own. If User A needs access to edit content as well as to  create content, you can assign User A to both the "Author" role and the "Editor" role. This means that User B will not be able to edit any content generated from the content type except for his own (if he has the correct permission set for that).

Second, I would recommend taking some time to review the documentation for Workbench Access for more information on configuration and permissions.