First of all, Bush wasn’t caught flat-footed. Condi Rice warned about this Soviet adventure months ago.
Second, sending in troops would have made the situation even more dangerous. I hardly think Putin would have been frightened away. And would the American troops actually shoot at the Georgians? Doubtful.
Putin was trying to exercise his power. Also trying to prevent Georgia from joining NATO. I don’t think 500 troops would have mattered although it would have warned Russia where NOT to shoot toward.