The Queen was a ret-con, which IMO worked for FC, but not for VOY or what followed (Scorpion was best because it lacked the Queen; there were rumors that the Borg's vulnerability to 8472 was because of lacking the Queen--sadly the later VOY eps showed that the Queen introduced stupidity in the form of petty jealousy etc.)
Anyhow, it's an interesting question, one I pondered after FC. I thought of several possibilities, but more on that later.
One other detail is...Picard seemingly 'just remembered' the Queen in FC, and had never mentioned him before.
Picard says: "I remember...you were there all the time" or something like that, and then "but that ship...and all the Borg on it were destroyed."
To which the Borg Queen replies, "You think in such three-dimensional terms. How small you've become."
Very enigmatic, but now I think the idea of how Picard had amnesia about the Queen is a disconnect, much like how the Queen somehow 'allowed sleep' in BoBW. So, it's possible that...
1) She was not physically there, she just was a manifestation of the Queen consciousness. There is however a flashback to the Queen seducing Locutus, was that virtual reality or what?
2) She was there, and tried to convince Picard to join them willingly, somehow. Actually I have a strange vision of her adopting a humanesque facade, like the real Alice Krige, or sort of like Vina in "The Cage" to get Picard to join her.
Anyhow, that leads to the possibilities on her involvement in the end of BoBW:
A) She was disconnected from the hive after the regeneration cycle began. Perhaps this was like the ending of "Dark Frontier" where the Queen is powerless as her command interface is disrupted. The drones freeze, while the Queen looks around herself helplessly and her control over the Borg shielding is disrupted. It is only momentary however, it seems. But maybe she developed that ability after BoBW.
B) Borg Queen escapes, as seen in the Shatner/Reeves-Stevens novel, "The Return" where a Borg escape transporter beam is used IIRC, and she just transports back to the DQ as the ship explodes.
C) Borg Queen is killed. Perhaps the 'regeneration' cycle caused her to freeze like a statue, just as the other drones went into hibernation.
Also, it's possible that the Queen was far less active in BoBW. Perhaps an earlier version of the Queen, much less sophisticated, brought out only for seduction. Note how they needed Locutus to address the others, and whenever shown Locutus was alone or with drones (except for the FC brief flashback). Perhaps the Queen was only briefly used, then shut down.
It would have been interesting to see a 'TNG Queen' where the EFX, costumes were different. I liked how the Borg look has evolved, however in 'Dark Frontier' and others there was a ret-con not only in the Borg appearance, but also the Federation consoles as seen on the Raven.
In the end however I would like to see some of the VOY damage to the Borg undone. I want to see the Feds defeat the Borg, but in a heroic and intelligent way, not 'cheating' with quick techno fixes and time travel/breaking the Temporal Prime Directive.
It was such a contrast from the faceless, deadly enemy in TNG that hailed the Enterprise, with the 'Dragon lady" dictator that hailed VOY in "Unimatrix Zero" and had the Queen say "stay out of what doesn't concern you." Laughable.
I propose a scene for the comeback of the Borg, where the collective themselves subsume the Queen as a defective program which has not benefitted the collective. In every single instance we've seen her deployed--either to seduce Picard/Locutus, to stop First Contact/seduce Data, to seduce Seven to their side, to stop Janeway, she's failed miserably. The only time the Borg do well with individuals is when they are assimilated for their knowledge (Locutus/Wolf 359) or used for limited negotiation purposes (Seven of Nine/Scorpion). Otherwise, it is better that the will of the collective be used; it frightens individuals into submission and is a lot harder to target than a single Queen individual. Not to mention a lot more scary, alien, and faceless to have the collective voice hailing you.