become a member of the Brotherhood of Steel as well as gain access to their safehouse. EDIT:actually no,that's the safehouse key,sorry.

If the player has a high enough reputation with the Brotherhood of Steel before destroying the bunker, Veronica will not leave. Code of Steel is a Brotherhood of Steel mod for Fallout New Vegas. Fallout: New Vegas The Abandoned Brotherhood of Steel Bunker The Abandoned Brotherhood of Steel Bunker. If the player destroys the Brotherhood bunker prior to meeting Veronica, then tries to recruit her, she will join the player, but almost immediately leave, saying that the player appears determined to fight the Brotherhood. You can get the inventory back by pickpocketing her, or killing her when she is walking away. It may be possible to get back the gear in her inventory by re-recruiting her (if that option is present), then immediately accessing her inventory via the companion wheel before she has a chance to speak to the player and leave again. Fallout New Vegas Caesars Legion Safehouse Key Legion Vexillarius armor, Legion.

Any items the player gives to her that she has when she leaves the player will stay in her inventory, and it may not be possible to get them back. As with the Brotherhood Safehouse, this will be near the map boundary. Fallout: New Vegas Walkthrough Caesars Legion Serving Caesars Servants By Nathan Garvin For Auld Lang Syne Render Unto Caesar This section will cover the end-game quests for Caesar’s Legion, starting after you destroy Mr. House and Caesar's Legion main quest lines it will be necessary to destroy the Brotherhood of Steel bunker in Hidden Valley, which will usually (but not always) cause Veronica to leave the player permanently, even if she is waiting somewhere else at the time. According to the Fallout Wikia page on Veronica Santangelo she will leave you permanently when destroying the Brotherhood unless you have 'high enough reputation', but it isn't more specific than that (see bottom point):

Fallout new vegas brotherhood safehouse