By default all Bitbucket Administrators can edit and execute scripts. However, Script Edit permissions can optionally be restricted to a smaller set of users.
When this setting is disabled, all members of the System Administrators group, and any group with the Bitbucket Administrators global permission, can edit scripts (this is the default state after you install the plugin).
Enabling this setting allows you to control which groups can edit ScriptRunner scripts. Note that only groups with the Bitbucket Administrators global permission can be authorised to edit scripts. This means that you can restrict "edit script" access only to some of the Bitbucket Administrators groups, for instance those with System Administrator permissions only. Please also note that when you add new groups, only groups that already have Bitbucket Administrators global permission assigned will be suggested.
Members of System Administrators group have access to full functionality of ScriptRunner regardless of status of Script Edit Permission setting.