So what happens with her? You see her at the beginning but she's like "hey go see that guy" and she disappears FOREVER.

She sure did.
 

 I also expected Tenenbaum to have a larger role in the game. She seems to be only a transitional voice to provide continuity and facilitate your introduction to Sinclair. 

I'd be interested to know what happened to her. There is evidence to construct a theory either way:
 

1. Jack Ryan was artificially created to assassinate Andrew Ryan. We know part of his creation was rapid aging. I also assumed that another side effect was being tougher than normal human. It's the only way I could justify Jack surviving BioShock 1 and taking down an army of Splicers and Big Daddies. 
2. Delta was a prototype Big Daddy. Not as durable as the production models but still tougher than a normal human. 
3. If you wanted to build a sequel around the Mark Meltzer as he is initially introduced to us - he is a 100% normal human. It's tough to believe he could escape Rapture. I found it hard to believe he made all the way to Sofia Lamb. If you want to build a sequel around the Mark Meltzer / Big Daddy, that would be a game very similar in storyline to BioShock 2. 

@ZAPBoston: 
 

1. If you wanted to build a sequel around the Mark Meltzer as he is initially introduced to us - he is a 100% normal human. It's tough to believe he could escape Rapture. I found it hard to believe he made all the way to Sofia Lamb. If you want to build a sequel around the Mark Meltzer / Big Daddy, that would be a game very similar in storyline to BioShock 2.     

Although Meltzers story in the Something in the Sea campain is pretty sweet, i dont think his time in rapture would have enough meat to really work out as another sequel, even if it was like a parallel story to delta. I do think, however, that Meltzers story would be awesome DLC, even though you know the outcome. i feel like that could have some good potential.

He doesn't have any weapons or plasmids.
 
Also yea, I think Tenenbaum's dead.

She GTFO of Rapture.

they are gonna make another and she will be in it too.

Tenenbaum says she has to go help other people which is basically a giant neon sign saying "I WILL BE IN BIOSHOCK 3"

She is the playable character in Bioshock 3. The game will revolve around more stealth since she isn't all juiced up on plasmids, and isn't a superhuman. However, when she is backed up into a corner, she can and will talk the Splicers to a philosophical death. Instead of taking pictures or recording a video for research points, you will make audio recordings about how bad you feel and how much you hate yourself.