"It makes every moment bitter" is correct. That is simply how sentence order is when you use the "make" like that. Here are some similar sentences. "She makes every game fun." "Music can make people happy." "Soap makes your hands clean." "It makes bitter every moment," is correct, but it sounds too dramatic for ordinary conversations. People will understand it, but the other sentence I wrote about above sounds much better.

It makes every moment bitter is correct! If you were writing poetry than the other might be more normal.

Agree with Chris, you probably mean better. "It makes every moment better." I can't think of anything that makes every moment bitter, except for my in-laws.

It makes every moment better. (bitter - refers to taste e.g. The lemon tastes bitter.)

In normal conversation we would say It makes every moment bitter; the other one would more likely be used in a literary sense.