Using Bat/Bas Sheva (or Elisheva) for a 7th girl or 7th child who is a girl is purely a cutesy thing to do. As is naming your first Rishona (and yes, I do know a Rishona who is the first).
As to the one word vs two words: It technically, as per proper dikduk and usage in Navi, should be either two words or one hyphenated word. However, common convention spells it as one word.
As to the Bat vs Bas – as far as dikduk, not sure when it is, but it might actually be Bat in certain scenarios. But in general, most Ashkinazim resort to the Bat for convention’s sake.