Bridge is not writing Metadata to TIFF Files!

The following Photoshop script will batch all TIFF files at the top/root level of a selected folder, adding the word "test" in the description metadata (replacing any existing description). This writes the metadata directly to the file without opening the file into Photoshop, so it should be very fast.

#target photoshop;

var inputFolder = Folder.selectDialog("Please select folder to process");
if (inputFolder != null) {
    var fileList = inputFolder.getFiles(/\.(tif|tiff)$/i);
    for (var a in fileList) {
        setDescription(fileList[a], "test");
    }
}

function setDescription(file, descStr) {
    if (!ExternalObject.AdobeXMPScript) ExternalObject.AdobeXMPScript = new ExternalObject('lib:AdobeXMPScript');
    var xmpFile = new XMPFile(File(file).fsName, XMPConst.UNKNOWN, XMPConst.OPEN_FOR_UPDATE);
    var xmp = xmpFile.getXMP();
    xmp.deleteProperty(XMPConst.NS_DC, "description");
    xmp.setLocalizedText(XMPConst.NS_DC, "description", null, "x-default", descStr);
    if (xmpFile.canPutXMP(xmp)) {
        xmpFile.putXMP(xmp);
    }
    xmpFile.closeFile(XMPConst.CLOSE_UPDATE_SAFELY);
}

If the previous script doesn't work for you, then we can open the files into Photoshop, add the metadata to File > File Info and then save/close the file, but that would be slower. This adds the keyword "test" replacing existing keywords:

#target photoshop;

main();

function main() {
    var inputFolder = Folder.selectDialog("Select the folder to process:");
    if (inputFolder === null) return;

    // Add or remove file extensions as required
    var fileList = inputFolder.getFiles(/\.(jpg|jpeg|tif|tiff|psd|psb|webp|png)$/i);

    for (var i in fileList) {
        open(fileList[i]);
        var theKey = ['test'];
        activeDocument.info.keywords = theKey;
        app.activeDocument.close(SaveOptions.SAVECHANGES);
    }
}

Both of these scripts are just hacks to see if bulk updating the metadata in Photoshop corrects the misbehaviour in Bridge, which you shouldn't need to do.