Is the right to bear arms limited by a national disaster, such as a pandemic? Certainly the freedom of travel and the right to peacefully assemble are curtailed. However, firearm rights in a national disaster are specifically protected under state and federal law. Much of the legislation protecting gun rights in a disaster stem from problems during hurricane Katrina where local authorities went door-to-door confiscating firearms. 
According to the New York Times, the New Orleans police decided that after a week of lawlessness in the city, no civilians would be allowed to carry pistols, shotguns, or other firearms of any kind. The police chief explained: "Only law enforcement are allowed to have weapons."
In response, the US Congress enacted the Disaster Recovery Personal Protection Act the following year (later passed as part of the Stafford Act). This law provides that no officer or employee of the United States while acting in support of relief from a disaster or emergency can seize a firearm that is otherwise legal to possess. The statute also provides for severe civil penalties for government agents that violate the law. The law also applies to agents of state and local governments if their agency received federal funding (so pretty much every police agency). The law was not particularly controversial. It passed by an overwhelming majority. Barrack Obama and Joe Biden where both senators in 2006 and they voted in favor or it, although then Senator Hilary Clinton opposed it, as did Senator Schumer.
Since this 2006 law, the right to bear arms in emergency areas has come up from time to time. For example, in 2017, in advance of hurricane Irma, the governor of the Virgin Islands signed a declaration that provided that authorities "could seize arms, ammunition, explosives, incendiary material and any other property that may be required by the military forces for the performance of this emergency mission...." That provision was never implemented, and it was widely questioned and criticized. The governor later explained that he intended the clause as authorizing the requisition of firearms rather than their seizure.
The subject also arose last week, during the coronavirus pandemic, when the city council of Champaign, Illinois authorized the mayor to "order the discontinuance of selling, distributing, dispensing or giving away of explosives or explosive agents, firearms or ammunition of any character whatsoever." No steps were taken to act on that language, and the wording was widely criticized. I would guess that a lot times when these declarations are put together, the officials just hastily grab some prior declaration that another city has used in the past. It is hard to say.
In Washington state, there used to be a provision granting the governor the power to prohibit "possession of firearms or any other deadly weapon by a person (other than a law enforcement officer) in a place other than that person's place of residence or business." However, that provision was repealed and it is no longer in the list of the governor's emergency powers. (See RCW 42.06.220). It is possible that local governments in Washington have come up with their own declarations of emergency that might address firearms. We will have to see.