They were both still around after the destruction of the second Beis Hamakdush. Rav Yehoshua who died about sixty years afterwards was unwilling to pasken on a machlokes between Beis Shamal and Beis Hillel saying he was unworthy (Yevomos 15B). The Gemora also mentions Rav Akiva and other Tannaim who died about sixty five years after the destruction of the second Beis Hamakdush discussing with Rav Dosa Ben Horkonos about whether the halacha is like Beis Shamai or Beis Hillel about Tzoras HaBas. He told them that his younger brother Yonasan Ben Horkonos is a Talmid of Beis Shamal and he was the one who gave the pask to allow it but they should not argue with him due to him greatness in learning (they did anyway) (Yevomos 16A) Etc.
Presumably Beis Shamai closed after the Bas KKol said that Halacha is like Beis Hillel (Eiruvin 13B) Although there is one opinion in the Gemara (see below) that even after the Bas Kol, Beis Shamai continued to follow their own rulings they probably did not get new Talmidim afterwards. So by default everyone joined Beis Hillel.
The Gemora does not say when that happened but it happened early enough in time that by the first generation of Amoriam (Rav and Shmuel) they were no longer certain about whether Beis Shamai went in accordance with their own rulings or not (Yevomos 14a-the Gemora concludes that they did)
Being that Rav and Shmuel died about two hundred years after the destruction of the second Beis Hamakdush and one hundred and forty years after Rav Yeshoua and Rav Akiva it must have happened soon after the death of Rav Akiva, Rav Yeshoua and that generation of Tannaim. Otherwise by the first generation of Amoraim they still would have been familiar with the practices of Beis Shamai as they would have been recent enough history
(Timelines in this answer are estimated and not exact)