Hi torrykones, welcome to the forum!
I haven't used the bird shipping service you mentioned, so I can't give you a direct answer.
In my personal opinion, I think it is a good idea to let a friend or a neighbor to take care of your bird in this situation. Give them very detailed yet easy to follow instructions should be good to go. You are only leaving for a month or maybe a little longer. It is not that long. For the extra cost to ship the bird back and forth, you might as well give it to someone locally to as compensate for their time. Just a thought. 
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