How the FHE encrypts a k-bit message just with one-bit encryption scheme?
One-bit FHE schemes, as you call them, are actually sufficient to implement a full adder.

You just have to encrypt each bit of the messages, then use the homomorphic logic gates to execute the circuit that you want.

For instance, if you have 2-bit messages $a = (a_0, a_1)$ and $b = (b_0, b_1)$, just encrypt the four bits, obtaining $c_{a, i}$ and $c_{b, i}$ (for $i = 1, 2$), use the homomorphic logic xor gate to add two bits and logical and gate to obtain the carry, that is, representing XOR by + and AND by $\cdot$, we have

First bit of the result: $r_0 := c_{a,0} + c_{b,0}$ (thus, $r_0 $ encrypts $a_0$ XOR $b_0$)

First carry: $c_0 := c_{a,0} \cdot c_{b,0}$

Then, second bit of the result: $r_1 := c_{a,1} + c_{b,1} + c_0$.

Second carry: $c_1 := (c_{a,1} \cdot c_{b,1}) + (c_{a,1} \cdot c_0) + (c_{b,1} \cdot c_0)$

Third bit of the result: $r_2 := c_1$ (just use the last carry as the most-significant bit)

Therefore, the resulting message is $(r_0, r_1, r_2)$.

You may want to check the TFHE project. They implement several circuits homomorphically (in particular, in the tutorial that link, you can run a circuit that computes the maximum of two values).