So I want to get Veronica to unlock Elijah's holotape so I can get Elijah's rambling perk, but every time I talk to her she says "couldn't get enough of talking to me the first time huh?" and my only option is "goodbye" so am I just screwed or is this a bug of some sort.

Both. It is a bug, and you are screwed. I could tell her about Elijah right away. Can you even recruit her now? Maybe you could reload an older save, but I have no idea if that'll change anything. :sadvaultboy:

I had to exhaust every single dialog option with her, then get out of the conversation, and then dig *again* into the dialogs until "I found Elijah" popped up at the bottom of one of the lists.

The integration is quite poor.