We know that bilqis accepted Islam after she met prophet suleiman. Do we have information on bilqis continuing as queen after acceptance of Islam?
No people who appoint a woman as their leader will ever prosper.” (Reported by al-Bukhaari, 13/53)
المرأة بلقيس بنت شراحيل
I know of no information which can help us draw conclusions if she continued ruling as a queen or not. I am not even sure what you mean with "information" either, is that limited to ahadith or stories from other faiths/cultures?
What is mentioned in the Quran (Surat An-Naml) is Solomon informing them (and her) to surrender:
Exalt not yourselves against me, but come unto me as those who surrender.
(Notice some interpret it as surrender as muslims)
The story continues to mention that she converted:
My Lord! surely I have been unjust to myself, and I submit with Sulaiman to Allah, the Lord of the worlds.
It is mentioned in the Wikipedia article that:
Muslim commentators such as al-Tabari, al-Zamakhshari, al-Baydawi supplement the story at various points. The Queen's name is given as Bilkis, probably derived from Greek παλλακίς or the Hebraised pilegesh, "concubine". According to some he then married the Queen, while other traditions assert that he gave her in marriage to a tubba of Hamdan. According to the Islamic tradition as represented by al-Hamdani, the queen of Sheba was the daughter of Ilsharah Yahdib, the Himyarite king of Najran.
We don't know if she continued to rule as a queen, or received a higher political position by Solomon.
But considering her being a political figure wouldn't been surprising because she once was the Queen of her people, therefore a good strategy would of course be to let her keep a higher position to rule her people, within and under the laws of Solomon. But this is only speculations.
If anyone has sources claiming her to continue to rule as a queen, please inform me.
In Islam there is a terminology called allegiance.
Muslims at times of their respective prophets give allegiance.
Prophets are default leaders or amir ul mumineen.
When tribal leaders of Arabia gave allegiance to prophet of Islam Muhammad, peace be upon him, they accepted him as their leader
Therefore Queen of Sheba gave allegiance to prophet suleiman by accepting him as prophet she also accepted him as leader. It's unimportant that she remained a Governor.
Conclusion: geographical area under Queen had a new leader , Prophet suleiman