In French, if you are leaving for only a few minutes (running an errand), is it better to say "A bientôt" or "A tout de suite"?"?

As a native French person, I would say: '' A tout de suite '' ...

"À bientôt" is too imprecise and will not convey that you'll be right back. It doesn't even indicate if you'll be back on the same day. A less common equivalent is "À tantôt".

"À plus tard", for me, is only a little less imprecise than "À bientôt" . It does indicate that you will be back the same day, but that's all.

"À tout à l'heure" is good, but it could mean you will see in a few hours. It would be a little weird if you're only back in 10 minutes.

"À tout de suite" is perfect for this situation. It's really about being back shortly. The informal version is "À toute".

I would prefer to say: "à tout à l'heure". 

"A bientôt" is too far away, and "A tout de suite" is just heavy, to be honest. 

"A plus tard" also works.