Hi Domdom,
Way back, my little sister read the Bunty, a British weekly comic for girls, which featured cut out clothes for Bunty. If you haven't seen these, there are plenty of pages on line. This site carries a selection:-
https://www.pinterest.co.uk/pin/389420699001513917/
As Bunty was published by DC Thomson, we can't host the title here.
Having watched hundreds of 1930s-1950s UK films, and a fair amount of UK TV series from the 1950s-2000 or so, and read some UK comics, as well, I'm familiar with "Bunty" as a fairly common (at least it was during the 1940s-1960s) girls' nickname. But, usually, most commonly used nicknames are shortened versions of legal Given (first) names. I can't, for the life of me, remember ever hearing what name "Bunty" is the shortened version. I remember that one of Chesterton's Father Brown amateur detecting assistants on some of his cases, here and there, was named Bunty.
Can any of you Brits inform me on that question?
PS - after a little research, it is as I expected, that it is related to baby bunting, but I also learned that both of those were derived from the same Medieval Scots root, "buntin", meaning plump and healthy - which often described a healthy baby.