The "bubble" has only been building since Jan 2001 (guess what happened then?) See http://en.wikipedia.org/wiki/File:USDebt.png. It's clear that if Clinton's policies were extended, the public debt would have gone close to ~0.

US debt is just government bonds, etc. The US govt holds China's money, and promises to pay the interest on those bonds when they mature. China owning US bonds actually makes it harder for them to purchase companies and properties in the US (they have a limited amount of free capital). If anything, the Chinese would avoid buying US companies - they would much rather concentrate on building up their own companies.

The Chinese have a few 100 billion dollars invested in US bonds (a tiny fraction of US GDP) mostly because it is a very safe investment. Why is it so safe? Literally, the only reason is that the US can print more money to pay back its debt. US bonds are the safest place to keep money because the US has proven to be such a stable country. Worst case scenario (other than the US collapsing, which is not likely), is the government will print more money and devalue the dollar.