Which term is used to denote boldness that crosses into rudeness?

The term that denotes boldness that crosses into rudeness is "presumptuous." This word describes behavior that is overly confident or forward, often to the point where it disregards the feelings or rights of others. When someone is presumptuous, they may take liberties or assume things that are inappropriate or unwarranted, leading to a perception of rudeness or overstepping social boundaries.

In contrast, the other terms—respectfulness, modesty, and submissiveness—carry connotations of humility, deference, or politeness. Respectfulness implies a regard for others and their feelings, modesty involves a lack of arrogance or self-importance, and submissiveness suggests a tendency to yield to others or avoid assertiveness. These terms do not capture the same sense of boldness that veers into rudeness as "presumptuous" does.