Well, the first thing that makes this story dubious is that US Treasury bonds (30-year bonds) quit being issued as bearer bonds on paper in 1982. That means that the holder would have to have accumulated quite the stash of these from the early 80’s - and a limited set of years: 1980, 1981, 1982.
But the 30-year was most heavily issued from 1977 until the 30-year was pulled from offering at all by the Clinton administration, who “compressed” the US debt into the shorter end of the curve.
OK, so how much bearer bond debt was out there? The best indication I can give you comes from the Depository Trust Company. In 1991, they had 600 people clipping coupons on bonds held by the DTC in trust for their owners and mailing in the coupons - on about 21 million bonds. As of today, the number of bearer bonds still valid and on deposit with the DTC is about 700,000 and the face amount is about $3.5 billion (and dropping rapidly). So that gives you an idea of the relative rate of drop-off of the instruments among people who are above-board and legit.
Further, when you send in a coupon to get your payment on the debt, or you send in the bond to recover the face value, the US Treasury takes down all manner of financial ID for US citizens. The only way you’re going to make one of these bonds good is to take it to a bank that is willing to present it to the US Treasury without invoking your name as the true owner.
And here, I think I’ve found the US Treasury’s report on the bearer debt outstanding:
http://www.treasurydirect.gov/govt/reports/pd/pd_bearregsec.pdf
There isn’t (according to the Treasury) enough bearer debt outstanding to meet the figures in the press.
As to not breaking up the shipment: See above. They amount they have is close to, or above, the total amount of US Treasury Bearer debt left outstanding from the period in which it was issued. There isn’t enough paper outstanding.