With the pro version of the WordPress AI Alt Text Generator Plugin you can bulk generate alt text for an unlimited number images.
To do this, use the Quick Actions menu found on the License settings page.
The Bulk area of the settings page gives you full control over this action. There you can choose to skip images with existing alt text, include/exclude specific folder paths and limit the number of images.
Scheduled Regeneration
If you would like to run bulk generation automatically, you can also set the Cron Interval (on the same settings page, seen in the screenshot above).