Scottish Gaelic/Irish: ma'am, sir, miss

[NerdTableforone]

In true American hypocrisy, many people still used feudal titles whilst decrying the system's inequalities. I, however, am one of them. With a Southern mother, I was trained to say them habitually. How would I do this in Scottish Gaelic/Irish? If not done, would I just ignore the title, use the name, or use the English?

Thank you, ma'am.
Tapadh leat, [word I do not know]/ma'am/NicDhòmhnaill.

I know some languages do not use them, but I always feel rude. Is there any other word that can be used instead?

Thank you, truly.
Tapadh leat, [different word].

 

[Pedro y La Torre]

Go raibh maith agat, a bhean uasal (Thank you, ma'am) is, I think, what one would say in Irish. The Scottish form would be similar Tapadh leat, a bhean-uasal.