After an unusually itinerant career, Mr Bradley had plenty of options for launching his campaign. He could have chosen Montclair, the New Jersey college town and dormitory for New York, where his wife teaches and they keep a flat; or Trenton, the capital of New Jersey, the state that elected him for three consecutive terms in the US Senate; or even Washington, where he spent the bulk of those years. Equally, he could have followed the example of the early Republican favourite, George W Bush, and chosen a folksy political setting, such as a state fair, in one of the key primary states, Iowa or New Hampshire.
But he settled on Crystal City, Missouri, a small town of 4,000 souls and white clapboard houses some 27 miles downstream from the industrial port of St Louis, within flooding distance of the great Mississippi. "You are what you come from," the aspiring President told his adoring audience last week, "and I come from Crystal City."
Named after the glass that provided its sole industry, the town has lost its one factory and succumbed to the fate of so many small US towns: bypassed by motorways and strip malls, its small shops and businesses gradually gobbled up by national franchises. The last independent businesses - a local pizzeria, three barbers and two bars - are just hanging on, the proprietors grumbling about the cheap prices and television advertising of their giant competitors.
More fortunate than many small towns, Crystal City is still alive, thanks to its proximity to St Louis, capitalising on its sense of peace and community as a haven for families and retired people. Mississippi Avenue, the meandering main street, shaded by oaks, still has the remnants of a centre: the square stone bank that Mr Bradley's late father once managed, the solid Presbyterian church, newish town offices and the fire station, as well as the schools that the budding sports star attended. Below is farmland, girded by the broad sweep of the river's flood plain.
When Mr Bradley returned last week, it was 38 years since he had shaken the sand of Crystal City off his feet, heading for Princeton University and a wider world that he would eventually anchor in New Jersey. But he never neglected his ties, even after his parents retired to Florida, visiting an aunt and old neighbours and friends, and never selling the stone-built family home with its basketball hoop in the yard. It was this house that he used as his base last week - incontrovertible evidence that he "belonged".
Whether he kept the house out of affection, inertia or political calculation, or a little of each, he well understood that a small-town past is a political asset in US politics. The voters like their presidents to come from somewhere definable, preferably somewhere like where they come from themselves.
The modest Truman house in Independence, at the opposite edge of Missouri from Crystal City, is a shrine to that president's homely style. At Johnson City in the high plains of Texas, visitors may see the hovel from which Lyndon Johnson started his trudge to the presidency, and the hilltop ranch to which he returned as LBJ, with its views to infinity and its rich man's toys: special-breed cattle, vintage cars, aircraft hangars and landing strip.
From George Washington's ponderous mansion at Mount Vernon, through Thomas Jefferson's self-designed gem at Monticello, to the small white timber house in Hope in the back end of Arkansas where Bill Clinton was born Billy Blythe, US Presidents have remembered and promoted their origins - the more modest the better - as part of the national myth known as the American Dream. Mr Clinton's campaign documentary, and the words he spoke at his nomination, "I still believe in a place called Hope", are classics of the genre.
Nowhere are small-town origins so prized and so politically marketable as they are in the United States, except perhaps in France. But here the asset is regional loyalty and distinctiveness. For Americans it is the received memory of a golden age when small-town values - modesty, decency and community - were the rule, when childhood was innocent and the wider world could be kept at bay.
It is not just politicians who find the home-town myth expedient. The film star Kim Basinger bought the whole town of Braselton (population: 418) in her native Georgia for pounds 12.5m, though she sold it six years later for only pounds 2.7m after a breach-of-contract judgment bankrupted her. In most cases, however, the association is more profitable.
Hope, a modest town that lived by its railway and was all but dying when the line closed, has a new lease of life thanks to President Clinton: not because he personally pushed public funds in its way (as a French politician might towards his home region), but because of the outside interest and commerce it has brought. The defunct station building is now shared by a railway museum and a collection of Clinton memorabilia. Harry S Truman had his presidential library built at Independence, where it is at the heart of a small college campus.
Those without such origins must find them where they may. George W Bush has the choice of Midland, Texas, or his father's estate at Kennebunkport in Maine, neither of which quite communicates the small-town message: no wonder he has his eye on a ranch. Al Gore is superficially better off. He owns an estate at the small town of Carthage in Tennessee, where he made his formal declaration of presidential intentions earlier this summer.
Mr Gore, though, is not universally embraced as a Carthage native. The family estate is tucked away from the centre, and he grew up in a hotel in Washington, where his father was also a senator. With the death of Al Gore senior, ties with his putative home town weakened further. The Vice-President is seen more as a Washingtonian than as "one of us". The warmth and pride so tangible in Crystal City last week, even from the Republican mayor, were missing in Carthage.
When Bill Bradley came to call on his home town last week, there were home-made welcome signs in every yard, flags on every building, and rows of tiny candle lanterns, native-Indian-style, lined the main street after dark to guide the native son home. "Crystal City gave Bill Bradley a hug yesterday, a big hug," intoned one local radio reporter, adding almost as an afterthought: "And a kiss."