I find it very telling that your primary definition of tznius… the “first word that comes to your mind,” if you will, is shame.
Busha means shame and is almost always used negatively.
Tznius and Busha are two distinct middos. The poster made an error by defining one using the other. Both middos have a positive connotation, and when possessed in tandem enable one to achieve the pinnacle of Modesty.
Busha indeed refers to shame, or rather bashfulness, and is considered the mark of a G-d fearing person. It is busha that provides a person with the incentive not to sin. This idea is found in many seforim, not the least of which (for the sake of Mod80) is R’ Miller zt”l.