The Mishnah says that according to Beis Hillel the words B'Shachveha Uv'Kumecha is teaching us that Shema must be said while people are lying down in the evening, and while people are getting up in the morning.
( A slight difficulty is as follows. )
-1-The Gemora says (Daf 8b, Rav Yehudah in the name of Shmuel )that we Pasken like R' Gamliel, that the nightly Shema can be said until Amud Hashachar, the light of dawn.
-2-The Gemora says (Daf 10b, also Rav Yehudah in the name of Shmuel ) that we Pasken like R' Yehoshua that the morning Shema can be said until the 3rd hour, when the kings are still getting up.
-3-We Pasken like Beis Hillel who interprets B'Shachveha Uv'Kumecha to mean while people are lying down and while people are getting up.
But this interpretation, while lying down and while getting up, only reconciles with the Gemora's Psak that the morning Shema can be said while some people ( kings ) are still getting up.
If the Gemora wants to be consistent and Pasken that the evening Shema can also be said while people are going to sleep, then it should have Paskened like R' Eliezer who
said " until the 1st watch " ( and not like R' Gamliel who said it's the whole night until the light of dawn ).
Thank You
Beis Hillel says, "When people are lying down and when they are getting up." "Lying down," in other words sleeping, is done the entire night. "Getting up," meaning the act of getting out of bed from a night's sleep, is only done up to the first three hours of the day. "Getting up" does not mean being awake.
I believe this definition of Beis Hillel's statement should answer your questions. This definition of "lying down", meaning as long as people are sleeping as opposed to when people are going to sleep, is stated explicitly by the Rabeinu Yonah (1a in Dafei ha'Rif, DH "v'Chachamim").
All the best,
Yaakov Montrose