If you have two bulk searches (let's call them bulk search 1 and bulk search 2, for simplicity), there is a way to identify patents that are present in both bulk search 1 and bulk search 2 which involves the clever use of Workspaces and custom fields.
Firstly for each of your bulk searches, save them to separate Workspace folders within the same Workspace. This can be done by selecting "Save to Workspace" from the search results page and then selecting the appropriate folder from the "Save to Workspace" area and then clicking on the option of "Save to Workspace".
Once you have done this, go to the Workspace that contains these two folders. From here, select the "New folder" option.
From the "New folder" menu, go to the "Calculation folder" tab. Once here, call the new folder "Combined Bulk Searches" and combine the two Bulk Search folders with an intersection.
You will now be able to see all patents that are present in both bulk searches.