[Jotaku]

SAO Fatal Bullet is partially multiplayer anime game. It does have multiplayer mode but it is not a full multiplayer game that works like MMORPG. 
So this means that you can play sao fatal bullet without internet connection in Singleplayer mode.

Let me explain more about its multiplayer mode in details.
For co-op you can team up with maximum 4 people and clear dungeons together. Unfortunately that's mostly about PvE multiplayer. There are more more things you play with others in PvE, however, mostly they are not played.
In dungeon, there are many maps and modes like hardcore so you can enjoy.

There are also PvP multiplayer, and the game provide many modes and options for PvP multiplayer.
It allows you to go 4vs4 team deathmatch or boss fight (basically a team that did more damage to the boss wins, and meanwhile players are able to kill each other as well but that doesn't contribute to winning in boss fight mode). Also you can set additional options such as handicap, setting 5vs3 and so on prior to the pvp match in order to balance teams. And there is also a free for all mode which means 1vs1vs1... and so on.
The game does have ranked match. In ranked match the game doesn't start until it gets full with with 8 people. However in custom match it can start with at least 2 people so most people in this game play custom match instead of ranked match.
There are also 2 modes, hero and avatar pvp mode. Hero pvp mode is somewhat similar to Overwatch, you choose one out of given anime characters (e.g. Kirito) and play pvp matches. In avatar mode, it becomes more like RPG that you use your own character in PvP and gears and levels are not equalized in this avatar pvp mode (but there is a option in pvp multiplayer which allow you to minimize the gap between equipments like no chips between players).

Anyways for any kinds of multiplayer you can invite your friends to your room, and also allow you to create private room that only permitted players can join in.
Lastly we have lots of sao fatal bullet multiplayer gamers you can play with, please advertise yourself to make friends to play with.
Hope this helps!