A simple custom search bar could be made up from a TextEdit control and a search button control, contained within a horizontal Linear Layout. The code below is a very simple quick implementation.

search.js

var txtSize = 22;
 
//Called when application is started.
function OnStart()
{
    lay = app.CreateLayout( "linear", "FillXY" ); 
    lay.SetBackground( "/Sys/Img/BlueBack.png" );
 
    //Create a layout to hold the search controls
    laySearch = app.CreateLayout( "Linear", "Horizontal, FillX, VCenter" ); 
    laySearch.SetBackColor( "#000000" );
    laySearch.SetPadding( 0, 0.01, 0, 0.01 );
 
    //Create a TextEdit control for entering search text
    txeSearch = app.CreateTextEdit( "", 0.85 );
    txeSearch.SetTextSize( txtSize );
 
    //Create a search button
    btnSearch = app.CreateText( "[fa-search]", 0.1, -1, "FontAwesome" );
    btnSearch.SetTextSize( txtSize );
    btnSearch.SetOnTouch( btnSearch_OnTouch );
 
    laySearch.AddChild( txeSearch );
    laySearch.AddChild( btnSearch );
    lay.AddChild( laySearch );
 
    //Add layout to app. 
    app.AddLayout( lay );
}
 
//Called when the search button is pressed
function btnSearch_OnTouch( ev )
{
    if( ev.action=="Down" )
    {
        this.SetTextSize( txtSize-4 );
    }
    else if( ev.action=="Up" ) 
    {
        this.SetTextSize( txtSize );
    
        var searchText = txeSearch.GetText();
        app.ShowPopup( "Search: " + searchText );
    }
}

(Sample posted by Chris Hopkin in the Droidscript Forum)

This function is designed to search for a string in a textEdit.

It starts searching from the current position of the cursor and, if it finds an occurrence of the string, positions the cursor immediately before the occurrence.

An area immediately following the cursor is highlighted as the selected area.

If it does not find an occurrence, the cursor is positioned at the beginning of the text, allowing the user to search again from there if required.

findtext.js

function findtext(thisedt,sought)
//thisedt = textEdit to be searched.
//sought = string to be searched for.
{
   //both toLowerCase for case-insensitive search
   var lc = thisedt.GetText().toLowerCase();
   sought = sought.toLowerCase();
   //current cursor position is start for search
   var curs = thisedt.GetCursorPos();
   //only compare against the searchable range
   lc = lc.slice(curs+1)
   // try to find next occurence of sought
   var pos = lc.search(sought);
   if ( pos > -1)
   { 
      //we found it
      pos  = pos + curs +1
      thisedt.SetCursorPos(pos)
      thisedt.SetSelection(pos, pos+sought.length);
   }
   else
   {
      //not found - go to start of text
      //user can search again from there if required.
      thisedt.SetCursorPos(0)
   }
}

This function can be used in an app in the manner shown in this sample code

samplefind.js

var edt,fnd;
//Called when application is started.
function OnStart()
{
    //Create a layout with objects vertically centered.
    var lay = app.CreateLayout( "linear", "VCenter,FillXY" );    
    var hlay = app.CreateLayout( "linear", "Horizontal,FillX" );
    var btn = app.CreateButton("Find");
    btn.SetOnTouch(doFind);
    hlay.AddChild(btn);
    fnd = app.CreateTextEdit("show");
    fnd.SetHint("Find");
    hlay.AddChild(fnd);
    lay.AddChild(hlay);
    //Create a text label and add it to layout.
 
    var scrollEdit = app.CreateScroller( 1.0, 0.83, "" );
    //Create a textedit and add it to layout.
    edt = app.CreateTextEdit( "",1,-1,"Left,NoSpell" );
    edt.SetText(app.ReadFile("/android_asset/app.js"))
    //edt.SetBackColor("#ffcccccc");
    //edt.SetTextColor("#ff333333");
    scrollEdit.AddChild(edt);
    lay.AddChild( scrollEdit);
 
    
    //Add layout to app.    
    app.AddLayout( lay );
}
 
function doFind()
{
   app.HideKeyboard();
   var findstring = fnd.GetText();
   findtext(edt,findstring)
}
 
function findtext(thisedt,sought)
//thisedt = textEdit to be searched.
//sought = string to be searched for.
{
   //both toLowerCase for case-insensitive search
   var lc = thisedt.GetText().toLowerCase();
   sought = sought.toLowerCase();
   //current cursor position is start for search
   var curs = thisedt.GetCursorPos();
   //only compare against the searchable range
   lc = lc.slice(curs+1)
   // try to find next occurence of sought
   var pos = lc.search(sought);
   if ( pos > -1)
   { 
      //we found it
      pos  = pos + curs +1
      thisedt.SetCursorPos(pos)
      thisedt.SetSelection(pos, pos+sought.length);
   }
   else
   {
      //not found - go to start of text
      //user can search again from there if required.
      thisedt.SetCursorPos(0)
   }
}