Beit Shammai said that the reason he held that one should recite Kriat Shma lying down at night and standing up in the morning is because it says "B'shavkcha U'vkumecha" - when you go to sleep, and when you lie down. When you go to sleep, you sleep lying down, and when you wake up, you get up, you stand up.

So the gemara explains Beit Shamma's reasoning to say that had we meant that you can do it at the TIME of kriat shma, the pasuk would have written BaBoker U'BaErev, at morning and at night.

I'm not sure I understand this. How does that necessarily tell us the actual time for kriat shma? We had the discussion earlier in the gemara (2b) that the words "B'shavkcha U'vkumecha" mean very specific times (when the Oni eats his meal, certain times of the mishmor, etc.) If the pasuk would have said BaBoker U'BaErev, we wouldn't necessarily know that we're reffering to specific times?

You mean had it said boker and erev then we'd have a problem of not being able to determine what that meant specifically? Are you saying that in Beis Shammai's "if it meant that it should have said that" it actually could not have said boker and erev since those would be too vague for us?

Yes. Boker is a very vague term. I get up in the morning, true. But I also eat breakfast. So maybe kriat shma should be done when I eat breakfast. The words "B'shavkcha U'vkumecha" imply very specific times...when I get up and when I go to sleep.

You really think that had the Torah said boker that tannaim would not have know how to be meduyak and determine what exactly boker means?

Well, it did say "B'shavkcha U'vkumecha" for a reason.

Of course. But the reasoning of "if it meant X it would have said Y, but since it says W it means Z like I say" is not uncommonly used in the Gemara.