Do you have someone in your family that is willing to take the bird when you pass?
Because really if you don't have anything like that set up, either through discussion, or in a will. Having life insurance on you wont promise the money will be used to care for your bird.
I think the most important thing, is to find someone trustworthy to you, that would agree to take care of your bird. After then, get a small policy to cover those expenses. You can probably get pretty affordable term life insurance policy for 50k for pretty cheap. You definitely shouldn't need more then that for 1 bird. I would go less if they offer it.