How can I pass a variable defined in Illustrator to Photoshop?

If the script is running from Illustrator and you want to open Photoshop, then pass in a string, and run a Photoshop function:

//Illustrator as the script application
#target illustrator

var docRef = app.activeDocument;
var ORGselectedcolors1 = "Foo";

for ( var j=0; j < docRef.layers.getByName("+Shirt_Color").groupItems.length; j++ ) {
    if(docRef.layers.getByName("+Shirt_Color").groupItems[j].hidden == false){
        ORGselectedcolors1 = ORGselectedcolors1 + j +";";
    };
};

runPhotoshop(ORGselectedcolors1);

/**
* Opens Photoshop via Bridgetalk and runs psScript function 
*  a string passed from Illustrator 
*  void 
* 
*/
function runPhotoshop(s){
    //open Photoshop and run psScript
    var bt = new BridgeTalk();  
    bt.target = "photoshop"; 
    //a string var. Note string single, double quote syntax '"+s+"'
    bt.body = "var s = '"+s+"';"
    //the function and the call
    bt.body += psScript.toString() + "psScript();";
    //$.writeln(bt.body)
    bt.onResult = function(resObj) { 
        //returned from the Photshop function
        alert(resObj.body);
    }  
    bt.onError = function( inBT ) { alert(inBT.body); };  
    bt.send(8);  
      
    function psScript() {  
        
        alert("Photoshop Running. Variable sent from Illustrator: " + s)
        
        //add commands here
        
        //this is returned after the fuction runs
        return "Message from Photoshop—Done!"
    }  
}

if (!arguments.length) {
	function illstr(fileName) {
		function vbscriptFileContent(value) {
			return """Set app = CreateObject("Photoshop.Application")
			: app.BringToFront : fle = """" + File(fileName).fsName +
			"""" : call app.DoJavaScriptFile(fle, """ + value + """)
			: Set fso = createobject("scripting.filesystemobject")
			: fso.deletefile(wscript.scriptfullname)"""
		}

		/*regular ExtendScript Illustrator code*/ rslt = '0;4;5;6';
		vbs = vbscriptFileContent('Array(' + rslt.split(';') +')');
		with(fle = File(Folder.desktop + '/vbscriptName.vbs'))
			open('w'), write(vbs), close(), execute()
	}

	(bt = new BridgeTalk()).target = 'illustrator', bt.body = 'illstr = ' +
	illstr.toSource() + ', illstr(' + $.fileName.toSource() + ')', bt.send()
}
else alert([].slice.call(arguments))

I haven't tried this out, but declaring the variable at the beginning of your script should make it global, and available to the entire script. Another option would be to write the info to a cssv file and then read back the file in the PS portion of the script.

var bt = new BridgeTalk();
var specifier = "bridge";
bt.target = specifier;
bt.body ='\
var docRef = app.activeDocument;\
var ORGselectedcolors1 = "";\
\
//Identify Selected Colors\
\
for ( var j=0; j < docRef.layers.getByName("+Shirt_Color").groupItems.length; j++ ) {\
if(docRef.layers.getByName("+Shirt_Color").groupItems[j].hidden == false){\
ORGselectedcolors1 = ORGselectedcolors1 + j +";";\
};\
};\
ORGselectedcolors1;'

bt.onResult = function (response) {alert ( response.body)}
bt.onError = function (err) {alert(err.body) }
bt.send(3000);