I think it can mean both and the actual meaning depends on the context (though I'm no native speaker). I believe the word order might also slightly indicate the more possible meaning: שישה עשר לימונים, בבקשה would more likely mean "Sixteen lemons, please", while בבקשה, שישה עשר לימונים would more likely equate to "Here you go, sixteen lemons".
Here's how Duolingo Dictionary defines בבקשה: https://www.duolingo.com/dictionary/Hebrew/%D7%91%D7%91%D7%A7%D7%A9%D7%94/dfbb15a79f18aa681c9a1f55b6579008
Here you go seriously is not a translation into English that makes any sense in the context of Duo's lessons to date . I am a native English speaker living in Israel - The sentence in Hebrew is correct but Duo's offer of a translation for בבקשה as "here you go" should have been introduced in a different context
I'm not an Israeli, but I think the confusion here is with the English. בבקשה can be used when asking for something, (like please). But it is also used when responding to thanks (like you're welcome), or when giving something, such as the lemons in this sentence. A shopkeeper might say בבקשה as they hand over the thing you are buying. This is the meaning in this sentence.
But the English for it might vary between countries. I might say 'here you are' or 'here you go', but not sure if that applies in other places - eg USA.
So you are saying it's a cultural thing to say בבקשה when giving a customer an item, as a form of politeness? I may have heard it and it didn't register in my American brain. I was in Israel for a year but never learned to use it in that way other than to politely say please. I would like to get more info about this if it's used in all stores etc?
I don't know if all shop keepers would say it, but I can't think of any other way to be really polite when handing something to someone. Maybe some shopkeepers would say the Hebrew versions of "enjoy", "bon apetit", "good luck", and whatnot., depending on the purpose of the thing they handed you.
In Australia "here you go" is a coloquialism . I guess one might say that so is בבקשה when used this way - however this is a programme which is limited with its use and explanations - it really doesn't matter because with the opportunity to chat like this we all learn something ner