Script Help

With the Image Processor Pro,,, you can record a generic save as step to save  the same type of file you opened as shown below.  Or record a particular support type. You cane even save one of each type BMP, GIF, JPEG, PSD, ESP PDF, PNG, Targa and TIFF with a single key press

That is how the Image Processor Script works.  It can process as single image as well as a batch of images.   If the Output image exists it will create a new file and add a suffix to the file name. Here is the Function it uses when saving files to save only new file.   It generates the file names you want.   It starts with _1.  Adobe install the script you want.  menu File>Scripts>Image Processor... . 

///////////////////////////////////////////////////////////////////////////////
// Function: CreateUniqueFileName
// Usage: Given a folder, filename, and extension, come up with a unique file name
// using a numbering system
// Input: string for folder, fileName, and extension, extension contains the "."
// Return: string for the full path to the unique file
///////////////////////////////////////////////////////////////////////////////
function CreateUniqueFileName( inFolder, inFileName, inExtension ) {
	inFileName = inFileName.replace(/[:\/\\*\?\"\<\>\|]/g, "_");  // '/\:*?"<>|' -> '_'
	var uniqueFileName = inFolder + inFileName + inExtension;
	var fileNumber = 1;
	while ( File( uniqueFileName ).exists ) {
		uniqueFileName = inFolder + inFileName + "_" + fileNumber + inExtension;
		fileNumber++;
	}
	return uniqueFileName;
}

There is a better script on the web Image Processor Pro... which is a Plug-in script so you can record your setting in an Action step and not have to use its dialog to save your tiff files,  You could set as shortcut for the Action and save your files  via a key press like F2.  However, you will most likely need to use an Old version of Photoshop to record the Action.  The Action recorder in current version of Photoshop seems to have a problem recording Image Processor Pro.. Action step.  Even in old version of Photoshop where Photoshop recorded a step that works correctly the step in The action palette the action's Image Processor Pro... step looks like an empty step that Image Processor Pro... is not part of the action. Here is an Action I just recorded in CS6.  I Loaded that Action into PS 21.2 seen here.  I opened a PSD file in a testfoldet and press the F2 key a few times.  You can see after after the first TIFF file that a suffix was added startint with _01,

A simple modification to some old code did the job, let me know how it goes!

// https://forums.adobe.com/message/4453915#4453915

#target photoshop

main();
function main() {
    if (!documents.length) return;
    // var Name = app.activeDocument.name.replace(/\.[^\.]+$/, '');
    var Name = "Bamboo"
    try {
        var savePath = activeDocument.path;
    } catch (e) {
        alert("You must save this document first!");
    }
    var fileList = savePath.getFiles(Name + "*.tif").sort().reverse();
    var Suffix = 0;
    if (fileList.length) {
        Suffix = Number(fileList[0].name.replace(/\.[^\.]+$/, '').match(/\d+$/));
    }
    Suffix = zeroPad(Suffix + 1, 3);
    var saveFile = File(savePath + "/" + Name + "_" + Suffix + ".tif");
    SaveTIFF(saveFile);
}

function SaveTIFF(saveFile) {
    // http://jongware.mit.edu/pscs5js_html/psjscs5/pc_TiffSaveOptions.html
    // http://jongware.mit.edu/pscs5js_html/psjscs5/pe_TIFFEncoding.html
    // TIFFEncoding.NONE
    // TIFFEncoding.JPEG
    // TIFFEncoding.TIFFLZW
    // TIFFEncoding.TIFFZIP
    tiffSaveOptions = new TiffSaveOptions();
    tiffSaveOptions.embedColorProfile = true;
    tiffSaveOptions.byteOrder = ByteOrder.IBM;
    tiffSaveOptions.transparency = true;
    tiffSaveOptions.layers = true;
    tiffSaveOptions.layerCompression = LayerCompression.ZIP;
    tiffSaveOptions.interleaveChannels = true;
    tiffSaveOptions.alphaChannels = true;
    tiffSaveOptions.spotColors = true;
    tiffSaveOptions.imageCompression = TIFFEncoding.TIFFLZW;
    activeDocument.saveAs(saveFile, tiffSaveOptions, true, Extension.LOWERCASE);
}

function zeroPad(n, s) {
    n = n.toString();
    while (n.length < s) n = '0' + n;
    return n;
}