"Ich bin spätestens morgen Abend bei dir."
It's more of a question of context for when to appropriately use mit and bei as far as I can determine from talking to my German friend:
*mit dir - with you (I do something with you, I'm with you during problems/on this...)
*bei dir - by/at... (Ich bin Morgen bei dir = by/at your place; You have something bei dir = you have something with you near you/your body; I'm with you during problems/on this...)
mit dir - support in: sharing opinion, with you 'in mind'
bei dir - support in: company, close to a person
No, you can say bei dir with a purpose. Here are some more examples that my friend told me about...
Ich schlafe bei ihr.
Ich schlafe mit ihr.
First one says that you are sleeping at her place, but the second one states that you're having sex with her. That's when learning a language can quickly become a minefield, huh...
Keine Sorge. Ich bin bei dir.
Keine Sorge. Ich bin mit dir.
First one: "Don't worry. I'm next to you/beside you."
Second one is more mentally: "Don't worry. I'm with you (on this opinion/in mind/despite not being there physically).". Although the second one wouldn't be worded like that usually. The sentence should have more context.
Ich arbeite bei dir.
Ich arbeite mit dir.
^ first one: "I work at your place/in your company." and second one: "I work with you (co-worker/partner)."
Wir treffen uns bei dir.
Wir treffen uns mit dir.
^ first: "We are meeting at your place.", second: "We are meeting with you."
Hast du das Buch bei dir (or: dabei)?
Hast du das Buch mit (dir genommen)?
^ This is pretty much the same, but the first asks more directly if you have the book with you (in a pocket or somewhere close); the second is more "did you take it along?"
Sometimes there's little difference, sometimes there's a huge difference. It seems like we are just going to have to learn it "the hard way" - by immersion, reading plenty of German sentences, and learning how to recognize when you use "mit" or "bei."
I think, from what it sounds like, I'd just describe the difference as this: bei = close to you (as being in the same place as you), mit = doing something with you (not necessarily physically) or understanding/supporting you.
Really good question by the way. :)