Veronica won't walk around with me anymore

After I get out of the Hidden Valley bunker after trying to convince the elder and kill the four Brotherhood of Steel people waiting for me and Veronica there, Veronica just stands where she was when the fight ended.

I have tried telling her to wait and then to follow. That didn't work. I also tried dismissing her and finding her again. That didn't work either. What can I do?

Hmm, it seems like a stretch but try this:

Travel to Gibsons shack (the one from her quest) and use the terminal on the floor.Click on download research notes and she should magically reappear talking about what technology to go after. Just choose whichever one to make her a follower once again

If the Gibson's Shack fix does not work, you can use console commands to break her surge of consciousness.
From the Fallout New Vegas wiki:

At Hidden Valley, she may glitch and stay at the intercom and the door to the bunker will become locked. The following commands can be used to fix this glitch: prid 000e32a9 then SayTo player HVVeronicaEnter.

and

Sometimes she will randomly stop following the player after accessing her inventory. The following commands can be used to fix this glitch: prid 000e32a9, resurrect 1, disable, finally followed by enable.