Bullets traveling particle system like overwhatch soldier 76

I’ve a line trace weapon and I want create a bullet travelling effect like soldier 76 in overwatch.

I’ve created a bean particle system with speed parameter. The problem is that the line starts from source and travels to the target but I need something like a fixed line that travel from the source to the target like this Soldier 76 - Overwatch (Gameplay Funny Moments) - YouTube

What is the right approach to do that?