You do need to bring your machine because the purchase will be tied to your Apple ID and the machine ID. Just explain that you have very limited internet access and are unable to do it at home. Unless you want to, you don't have to install it while there - when the download is finished, quit the installer, find it in the Applications folder and copy it elsewhere for safekeeping. Then go home and launch the installer in the applications folder by doubleclicking it.
Make sure you have a backup of everything just in case.