I noticed that there's a permission :
You don't. Permission schemes are handled at a project level, not issue.
Two options both involve using the workflow to do something differently for the issue type. One is to do something quite sneaky with hidden fields and the workflow for that issue type, but it's really hard to get right and you need scripts. The other is to remove the due-date from the edit screen for that issue type and add transitions that say "change due date", with conditions that say "only reporter"
Instead of achieving this via permission scheme you can achieve the same behavior with workflow conditions.
Set up a transition on the same status (i.e. Open -> Open; In progress -> In progress ) and give permission only to reporter to perform the transition and then add transition screens with only the Due date field in it for these transitions. Of course you will need to remove the due date field from all other screens to disallow common users to update this.
Also update issue type screen scheme so this condition only applies to Bug not to other issue types.
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