When you are on the LookUp - 'Search History' section, click the checkboxes beside the name of the contact to select the contacts for which would like to perform a bulk action (see the below screenshot).
On selecting the boxes as shown below you will notice that the options to bulk add the contact will show in the center of the 'Search History' section.
You can proceed by clicking on the desired bulk function you would like to perform. From here, the steps to perform the bulk action to Save as a Contact, add to a Static List, Sequence or Tag are the same as those performed individually.
Note: The above example of contacts shown under 'Search History' are a few of my contacts that have been searched for using the 'Domain Search' (you have the option to filter your records under the 'Search History' by using the filter options to the right in the above screenshot).
The process/steps after bulk selection to perform any of the bulk actions are the same as the individual process mentioned in the below articles.