I'm currently trying to recruit Veronica and the only response I get from her is one line of dialogue to which I can only reply 'Goodbye'. Im guessing I must have bad mouthed the BoS in a previous conversation, but i've now completed Still in The Dark and i'm liked by the BoS. Have I missed my chance completely? BTW, I have no other followers with me whilst trying to recruit her.

You said that you had no other followers "with you", but do you have a current human companion that you have not dismissed yet? If so, you have to dismiss them to get her to follow you. I originally thought I could just tell Boone to wait somewhere and then go get Veronica, but I had to dismiss him first. I think I remember getting the "Goodbye" dead end with her until I dismissed Boone.

I've dismissed Boone and ED-E back to the Lucky 38 and I still get the same dialogue option with her.

If you told her that the Brotherhood is an enemy of the NCR, and that she should report them, I think she won't follow you.