It's artistic, and best not to think of it as literal.  "I got my ticket for the long way ‘round" implies that she's leaving, most likely for good, or an extended amount of time. 

"Two bottle ‘a whiskey for the way
And I sure would like some sweet company
And I’m leaving tomorrow, wha-do-ya say?"

She's basically saying "I'm leaving this place, who wants to come with me?"