The defense in OTL consisted of three lines. The first was weak militia and was soon routed. The second was placed (semi-legitimately) by Secretary of State Monroe, in a bad position, held for a time and also was routed.
The third line consisted of a naval battery and some sailors who had previously been skirting around the Chesapeake, now disgruntled and wanting to face the British heads on. Their position was fairly strong, and it temporarily managed to stem the retreating tide. According to various sources, somewhere along the line someone called for a retreat, and then the whole line gave way - only at this point could it be called the "Bladensburg Races".
For a very small BP, say that a very good commander, as far down as captain, although anything up to John Stricker, comes to the field just as the second line is retreating. This person urges a hard stand along with the naval people, and manages to rally easily 2-3,000 men in a good defensive position. The British did not number more than this, and so by slowly falling back until nightfall Bladensburg will be similar to the land battle for Baltimore.
Also, I dispute that it was the most shameful defeat in US history. Kip's Bay in the Revolutionary war had closer odds but was an even worse defeat.