The "fallout shelter boom," as it was, came in the 1960s, not the 1950s. The public enthusiasm for them followed a speech by President Kennedy in 1961, and there were many attempts by state and federal governments to encourage private shelters. The difficulty here is calling this "the US" — most of this effort was the result of private investment and construction, not coordinated (much less federally-funded) shelter development. (There were legislative pushes to have publicly-funded shelter programs, but they died in Congress.) Because it was private, it's hard to get a good number on how many were built, though one source puts around 200,000 by 1965, which is about one shelter for every 900 people, or one shelter for every 266 households. So that is neither particularly common nor particularly uncommon; it is a low number compared to the number of Americans who believed that nuclear war was likely to occur (slightly more than half of the population believed this). By the late 1960s the enthusiasm for private shelters had diminished, and instead there was a push in 1967 to identify private and public spaces that were adequately constructed to be useful for sheltering from radiation. The National Fallout Shelter Survey is why you sometimes still see "Fallout Shelter" signs in urban areas — those are the identified spaces, not purpose-built shelters, and some 160 million places were identified, mostly in heavily urban areas. (The irony here is that fallout shelters are not all that useful in urban areas, which would have presumably been primary targets of a Soviet attack, they would have been most useful in suburban areas that were downwind of these targets.)

The US never had much of a shelter program, because the people in charge of dispersing money for it (Congress) were never really convinced of their utility. As a result, it relied on far "cheaper" programs, like encouraging people to build their own, at their own cost. Some people did pursue this, but it was not especially common.

These numbers come from Kenneth Rose, One Nation Underground: The Fallout Shelter in American Culture (2001), 201-202, and 206.