According to this doc I should be able to find a checkbox that manages the rule to be executed in bulk but I can't find it in the current automation screen. Is there a way to activate it?
I'm using Jira cloud based.
As far as I see your screenshot is taken about Jira Cloud, but the link you pasted points to Jira Server/Data Center documentation. This explains the difference.
But, I think the "Run a JQL search and execute actions for each issue in the query" is the same feature that is called "bulk" on Server/Data Center. They're equivalent, but the labels are different...