There is no out of the box option to do a bulk download of artifacts.
However, there are several other ways to do this:
You can write a script that runs a Retrieve Artifact REST query on the desired artifacts.
Write a User Plugin that will download the artifacts based on the desired logic (download a folder recursively, or search by properties).
If you want to download artifacts from a certain build, you can easily search these artifacts by properties; if your builds were created by one of our CI servers integration plugins (Jenkins, TeamCity, Bamboo), these builds are deployed with the ‘build.name’ and ‘build.number’ properties. So with option 3, you can simply search by property and get all the relevant artifacts to export.
This can also be used with option #2, the script can be set to run the Property Search REST query, and then download the results.