All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
It is better for the person who drinks to combine between two things, drinking his fill of Zam-Zam water and drinking by three sips while breathing outside the container, and this is possible.
Ibn 'Abbaas said: "If you drink Zam-Zam water drink your fill, turn towards the Qiblah, say "Bismillaah" (in the name of Allaah) and breath three times and when you finish, you should say "Alhamdu lillaah" (All perfect praise be to Allaah)." [Al-Haakim]
The Sunnah when drinking Zam-Zam or any other drink is to drink by three sips. Imaam Al-Bukhari and Muslim reported that the Prophet used to drink in three sips, breathing outside the container. Ibn Qataadah also narrated that the Prophet forbade breathing into the container when drinking. When a person drinks in one go, he will possibly breath into the inside of the container (the thing which is forbidden).
Allaah knows best.