Actually very little bandwidth is required for most Aviation control related items. This is due to the substantial redundancy built into the "entire system." Each part plays a role in ensuring adequate control of the air traffic in the associated area. The FAA has over 30,000 stations around the US. They range from VOR's to weather camera's to AWOS (Automated Weather Observation Stations) sites, to regional ZAN's/ATC's. Regional ATC's require the most bandwidth but the FAA is just now getting out of the TDM world and moving to ethernet.
TDM, aka legacy circuits such as T1/DS1's, DS3's, and OC-3's, provided extremely predictable bandwidth that was completely serialized. The FAA took advantage of the serial nature of TDM and built an entire network of equipment, in excess of 150,000 unique service/location combinations, and it still works to this day. When digital bandwidth was expensive in the 1970's the FAA built most of its services to rely on 9600 bits/sec. Some things rely on only 2400 bps. With a 9600 bps requirement they could stack 5-6 services on a single 64k digital channel. This saved the FAA alot of money over the years.
What is more interesting is the detail the FAA has on each site. Of the 30,000 plus locations the FAA has on record they have a strict listing of the redundancy requirements, which generally translates into uptime requirements, for each one. In some locations a single circuit is ok. Other sites two circuits/connections are ok. In other sites two connections are required but they must be from different providers. In other sites the connections must be different providers, physically diverse from each other and terminate at different Central Offices. Going even further the FAA might require physically different transports or even three connections, all of which are physically diverse in all aspects. In the legacy TDM days the FAA would request a circuit path that would require the circuit to avoid certain central offices even when going across a small town. In some regional centers there will be multiple carriers with multiple physically diverse entrances for the remote connections.
That said the question is related to Traffic Control. The FAA needs very little bandwidth for traffic control. There are larger pipes, OC3's and OC12's, now moving to Gigabit ethernet, between the regional centers so they can share radar and traffic control data but generally speaking regional centers can operate independently, though that is far from ideal. Most of the data is not air traffic control though and even the centers migrating to gigabit ethernet are doing it for the cost savings, not the bandwidth needs. Telco's are raising their prices substantially for TDM (T1, OCx) services making it prohibitively expensive to stay on TDM Circuits. For voice traffic to the airplanes this is minimal. G.711 is ~90k when active but there are codecs that are more efficient. Most airline carriers have large networks that consist of remote SIP-to-RF radio's but most are single channel radio's so they would only need less than 100k when they are active.
That said the system has a massive amount of redundancy built into it to ensure that no one location knocks out the entire system. This is matched with the rules of flying that generally state the pilot is the one in control of the airplane and is responsible to be situationally aware at all times.
I know all of this because I work for a Telecom in Alaska that supports the FAA. Alaska has been a proving ground for the next generation equipment remote equipment for the FAA. Alaska's vast and remote distances pose significant challenges to the FAA in terms of reliability, both the equipment itself as well as the communications to that equipment, and the criticality of the equipment. In fact ADS-B was designed and tested in Alaska extensively before it was rolled out nationwide.
All said and done the bandwidth is not the issue for the FAA. Generally speaking control data is very little, be it in Aviation or controlling an oil field. The sheer number of sensors can add up, but it is nothing compared to the data a Netflix PoP pushes in a day.