tesoro, caro, amore, bambino

I'm confused, I need help from an Italian speaker. My partner and I tend to call each other darling even in public. Personally I feel awkard when she calls me by my name, it seems to lack the intimacy that we have being a couple.

So in English I would preface many conversations with "darling, what..." or "darling, have you...", you get the picture, and even when we're around friends and family we still call each other darling.

And that leads to the question, what is the equivalent Italian? The dictionary gives two translations for darling, caro and tesoro, but you hear Italians saying/singing amore or bambino. As I mentioned in another post, we want to speak Italian to each other as much as possible because when we eventually get to Italy we are quite likely to try out total immersion in the language.

So, opinions please, what is better?
"caro, ...", "tesoro, ...", "amore, ....", or "bambino, ..."

Thanks to Richard's comment below I can point interested readers to 'E niente, � niente, carissima!' and 'My dear ...'.