Normally you can share apps from iDevice to iDevice as long as they are on the same iTunes account. This is by far my most used app during the summer. I have used it multiple times daily during the season for the last 3 or 4 years.
I subscribe to MLB.tv so the At Bat premium app is included in my subscription so I'm not sure how it works if you get the app by itself. If they give you a MLB audio account you can just download the free version of the APP and log in with your MLB account. This allows you to log in on whatever devices you want so you would only have to buy it once and use it on iPhone, iPad, Android, PC, etc...
When you just get the audio by purchasing the premium app from the app store it might not work the same way. They might not actually give you an audio account and just give you access through your iTunes account only.
Edit:
http://mlb.mlb.com/mobile/atbat/ According to the official MLB website they do actually give you a cross platform universal audio account. You can log on with this account on PC/MAC, iPhone, iPad, Android, etc... Meaning yes you can buy it once and share it on multiple devices. You can also use it on multiple devices at the same time. Me and my Dad often have live game video or audio streaming at the same time on my account.
As for bandwidth, I can't give you an exact amount but I don't think you will see that big of a hit. We also have a Verizon share everything plan with 4GB of shared Data. We have 3 iPhones and 2 iPads sharing that data but even with all of that we rarely even reach 2GB. Between Podcasts, MLB at Bat, and Pandora I am almost constantly streaming something when I drive or when I sit at my desk at work. Of course, all of us do connect to WiFi at home and our offices so that has a big impact on the amount of bandwidth we use.
