Encoding of the message in Regev encryption
I think there are are several ways to do that. For instance, the "BGV-like" way is to embed the bit $a$ in a vector $\vec{a} = (a, 0, 0, ..., 0)$.

Then, the encryption is quite the same: $a \mapsto (Ar, Br + \vec{a}\lfloor \frac{q}{2} \rfloor)$. And to decrypt, you can subtract $SAr$ from the second component to get $v := Er + \vec{a}\lfloor \frac{q}{2} \rfloor$. Then, notice that $v$ is a vector whose the first entry is $er + a\lfloor \frac{q}{2} \rfloor$ where $e$ is the first row of $E$. Therefore, if you take the first entry of $v$, you get the same that you have in the original scheme and you can proceed as before.