Green’s Dictionary of Slang

1. to run off, to escape; to move at speed.

1821		‘An Amateur’ Real Life in London I 137: [He] grabb’d his pocket-handkerchief, and was after shewing a leg,† when a little boy that kept his oglers upon ’em, let me into the secret, and let the cat out of the bag by bawling—Stop thief! [†Shewing a leg—or, as it is sometimes called, giving leg bail—making the best use of legs to escape detection].
1837		R.M. Bird Nick of the Woods I 177: I’ll fight for you, or run for you, take scalp or cut stick, shake fist or show leg.
1840		T. Haliburton Clockmaker III 60: So we showed a leg right off, trotted down-stairs, and into the coach in no time.
1877		H. Hartigan Stray Leaves (1st ser.) 270: The fellow whom I had disarmed thinking discretion the better part of valour was showing a leg to escape.
1887		H. Caine Deemster I 221: He’d better show a leg if he don’t want the rat’s tail.

2. to dance.

1831

Navy at Home II 168: Some, even from among the blue coats; who had shewed a leg at the upper rooms at Bath, or at fashionable parties.