Verified answer

less direct to say "I was wondering" than "I am wondering."

We say "I'd like to have" rather than "I will have" when ordering in a restaurant. Your quote also uses "wanna" instead of the more formal "want to". So as a whole it feels more informal, less direct.

Grammatical tenses are like much else in the language, more a signal of formality / informality than strict time references.

Note your (very correct) rephrasing of the question

"My question would be " rather than "My questions is"

I was wondering if you want to have dinner with me -- implies you've thought of it already and now have the opportunity to voice the thought and ask you out.

I am wondering if you want to have dinner with me -- implies you just thought of it one second ago in the spur of the moment, like for example if the person who says this was asked just a second ago what he was thinking of. "what are you thinking of?" reply: "I think of the stars and... of my thesis. And I'm wondering if you want to have dinner with me, too", though even in this context, the person has already moved beyond the act of wondering so it already has become past tense, so "I was thinking/wondering if you want to have dinner with me", to me, would be perfectly OK too.

I would never say ' i am wondering', the phrase is ' i am just wondering' if it is an instant thought or ' I was wondering' if it was an after thought, and not with wanna. ' I am/ I'm just wondering if you would like to have dinner with me'.

Both are correct I was wondering is a past tense of the act

I am wondering is the present tense of the act

I think it sounds more casual.

It also just seems weird to still be wondering while you're asking---you've kind of moved on from merely wondering at that point, I guess.