Add keyboard shortcuts or items in bar

There is a (limited) way of adding shortcuts to Bridge.

In windows, I have managed to add them to specific iconbuttons on a UI panel I have created.

For example, adding a shortcut to a button that runs a script:

app.document.navbars.filesystem.top.visible = true; // if you don't wanto the menu to be visible, you can put this to false
app.document.navbars.filesystem.top.height = 40;
if (app.document.navbars.filesystem.top.length < 1) {
    var myBT = app.document.navbars.filesystem.top.add('iconbutton', [0,0,undefined,undefined], undefined, {style:"toolbutton"});
    myBT.size = [74,40];
    myBT.text = "My Button";
    myBT.fillBrush = myBT.graphics.newBrush(myBT.graphics.BrushType.SOLID_COLOR, [0.1, 0.1, 0.1, 1] );
    myBT.graphics.font = ScriptUI.newFont("Trebuchet MS",'regular',11);
    myBT.textPen = myBT.graphics.newPen(myBT.graphics.PenType.SOLID_COLOR, [189/255, 220/255, 215/255, 1], 1);
    myBT.onDraw = function (event) {
        with ( this ) {
            graphics.drawOSControl();
            if (event.mouseOver) {
                graphics.rectPath(0, 0, size[0], size[1]);
                graphics.fillPath(graphics.newBrush(graphics.PenType.SOLID_COLOR, [253/255, 79/255, 87/255,1]));
            } else {
                graphics.rectPath(0, 0, size[0], size[1]);
                graphics.fillPath(fillBrush);
            }
            if ( text ) {
                var mesure = graphics.measureString(text,graphics.font);
                graphics.drawString(text, textPen, (size[0]-mesure[0])/2, (size[1]-mesure[1])/2-1, graphics.font);
            }
        }
    }
    //
    myBT.onClick = function() {
        alert('$.evalFile(Folder.desktop+ "/my_script_to_run.jsx"); ');
    }
    //
    ////////////////////////////////////  this extends the right-mouse thumbnail menu at the end adding a prefix letter S, T. U, V, W, X, Y, Z (i used Z in this single example)
    if (MenuElement.find('myBt') == undefined ) { // the prefix fisrt letter is important to get what button you want to press
        var bt_Z = new MenuElement("command", "Z run my script", "at the end of Thumbnail", 'myBt');
    }
    bt_Z.onSelect = function () {
        app.document.navbars.filesystem.top.children[0].onClick(); // this runs the 1st button  on the top panel of Content
    }
}

How to trigger the shortcut?

Bridge can't help you. On windows you can intall a mouse control freeware tool. I use X-Mouse Button Control:

Then I create a listner within X-Mouse Button Control to Bridge application, selection my right-mouse button and the letter I want to add.

The limit is the number of mouse buttons you have available.

In the image I have assigned the middle button mouse to run my script >> just adding a Simulated Keys (release) putting the code: {RMB}X

RMB = right mouse button

Hope it helps!

I don't think there is an easy way for Bridge scripts.

The only way I can think of is to call a Photoshop script by a shortcut, and have the script call the Bridge script via BridgeTalk.