Overall this is pretty good. I can tell that english isn't your first language so I can give you a few grammatical tips by fixing some of your texts

"THE heart wants what it wants",

"To begin the liking process" doesn't sound like a normal thing to say. For me its really funny because its so explicit, but it would be better to say "Why don't we grab a drink sometime and see if we like each other"

"I live in THE bay area these days, but I come to LA every two weeks for work"

I think the daddy thing was great, not too aggressive and you played off her response well

Your last text where you said "I will plan accordingly" was not good, its not a normal thing to say for english speakers and it also shows neediness like you will arrange your schedule around her. What I would say instead is "I'll be in LA later this week, whats your schedule like" which is a lot more chill

Well, if this is a cold IG dm, this was way too much too fast. You went from bantering to hard closing in one text with no transition. A much better text would have been something more like "Btw. Guess where I'm gonna be next week". And when she says where, you say "LA". When she says "Cool", you say "Yea. We should grab a drink sometime soon". Something like that would have been much better