I recorded this and it works OK.

What I'm not liking is the .MoveUp to select the Bibliography field

It seems that there is the chance that the wrong thing could end up selected and therefore styled.

Is there a way to make certain that the Bibliography field is always selected?

Sub Macro1()
    Selection.Fields.Add Range:=Selection.Range, Type:=wdFieldBibliography, Text:=" \l 1033"
    Selection.MoveUp Unit:=wdLine, Count:=1, Extend:=wdExtend
    Selection.Style = ActiveDocument.Styles("MLA Reference")
End Sub