Check the permission scheme for the project - you need "delete issue" permission before it will appear.
However. Don't. Deleted issues are gone, permanently, forever. Delete the wrong thing and you could spend days arguing with backups, trying to get it back.
It should be limited to those you trust to get it right, or better, not allowed at all, with issue being moved to some sort of dustbin project.
Agree with Nic's response.
I would rather create a transition called "not a valid bug" or something in that line and link it to your "Done" status.
This way, you mark the bug as not feasible and can communicate to a customer as well has have a history of the bug.
Hope this helps.
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