Dax seems to have a remarkable grasp of ancient fables and superstitions, and she's obviously familiar with Iamblichus' Life of Pythagoras.
She's referring to two old superstitions which were first put together by the Ancient Greek philosopher Pythagoras. The first half of the line refers to the belief that it is unlucky to put your left shoe on before the right. The second half of the line refers to an ancient belief that the left side is somehow less virtuous than the right side. Bathing was seen as a somewhat base, mundane, and unclean activity, and so it was preferable to step into the bath with your left foot rather than the right foot.
It was at one time thought unlucky to put on the left shoe before the right, or to put either shoe on the wrong foot. It is said that Augustus Cæsar was nearly assassinated by a mutiny one day when he put on his left shoe first.
Put on the right shoe first. One of the auditions of Pythagoras was this: “When stretching forth your feet to have your sandals put on, first extend your right foot, but when about to step into a bath, let your left foot enter first.” Iamblichus says the hidden meaning is that worthy actions should be done heartily, but base ones should be avoided. (Protreptics, symbol xii.).
E. Cobham Brewer, Dictionary of Phrase and Fable (1898)
The actual quote from Pythagoras, and the explanation by Iamblichus:
When stretching forth your feet to have your sandals put on, first extend your right foot; but when about to use a foot-bath, first extend your left foot.
Explanation.--This Symbol exhorts to practical prudence, admonishing us to place worthy actions about us as right-handed; but entirely to lay aside and throw away such as are base, as being left-handed.