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, add a custom field that will identify each bulk search. This can be done by going to the "Custom Field" drop-down menu found in the top-right of the Workspace area and selecting "Add custom field".
From the "Add custom field" menu, give the custom field a memorable name, select the "drop-down menu" field format option and add two options for the drop-down menu which will make it obvious which custom field value corresponds to which bulk search and click on "Submit". You can see an example of this below.
Once you have done this, add the custom field value that corresponds to the folder to all patents in that folder. To do this, select the option of "Select all" and select the option of "Edit custom field" found in the bottom-right of the screen.
Then from the "Edit custom field" menu, add the custom field value that corresponds to the folder in question and select "Submit".
Once you have done the same procedure with the second folder (using the other custom field value and also making sure to show the same custom field as in the first folder), then copy the contents of each folder to a third folder. This can be done by selecting all of the patents in each folder and selecting the option of "Copy to" from the bottom-right of the screen.
From the "Copy" menu, select the third folder and click on "Submit".
If you then go to the third folder and show the custom field, any patents that appear in both bulk searches will have both custom field values.