It's hard to tell without seeing how your game is set up all together.
What I normally do is set up a master clock for the game, usually around 50fps (20ms per frame). Then to save myself the headache, immediately convert that into seconds at the start of my main step function, then pass the amount of time that passes to all the objects which need updating.
If you can move a maximum of one step per frame, that's still 50 steps per second. The answer is to move more than one step per frame, if you need to go faster.
Normally, I'd just make the bullet bigger than it would actually be, to represent the path it travels through in a single frame, but you can just say that if you're moving more than you can test in a single step, to do smaller steps in the same frame.
But if you turned the timer down to 1ms/frame, then the problem is probably not the bullet class, but the overall framerate. You can fix thisin the bullet class by moving more than one step per frame.

The link is throwing a 429 too much traffic error.
When I said more than one step per frame, I meant something like a loop or recursion. Obviously, you don't want to skip spaces, otherwise you get the bullets-going-through-walls problem that is an issue if not specifically planned for.

Like, here's a bit from the character class in my current project, in the part that handles movement:

    void always(double dt) {
        shape@ targ=this.bounds.translate(this.v.x*dt, this.v.y*dt);
        
        // (Bunches of other things...)
        
        if(!targ.intersects(this.bounds)) {
            this.v*=0.9;
            this.always(dt*0.5);
            return;
        }// moving too fast.
        
        // (etc)
        
    }// always.

But I also make sure my small objects have bounds that let them move at the speed I want. You can modify that bit to make it stay at the same speed, but it's important to be careful when using recursion like this.

So, your bullet class could have the move function use a loop, and when I say it moves more than one step per frame, it does the full movement check and everything for each step--it just does this 2 or 3 or 8 times per frame.