EDIT - How can I download a file with batch file without using any external tools?
I think Bitsadmin does not work with relative paths and you need to add full name to the local file.
You can check also my bitsadmin script thats spends a lot of dirty work - it accepts two arguments url and the path to the local file (and a timeout number - default is 5).As you can see the it pre-pend %CD% to the local file name:
   @echo off
    setlocal
   :download
   
    if "%2" equ "" (
      call :help
      exit /b 5
   )
   
   if "%1" equ "" (
      call :help
      exit /b 6
   )
    set url=%~1
    set file=%~2
    rem ----
    if "%~3" NEQ "" (
        set /A timeout=%~3
    ) else (
        set timeout=5
    )
    bitsadmin /cancel download >nul
    bitsadmin /create /download download >nul 
    call bitsadmin /addfile download "%url%" "%CD%\%file%" >nul
    bitsadmin /resume download >nul 
    bitsadmin /setproxysettings download AUTODETECT >nul
    set /a attempts=0
    :repeat
    set /a attempts +=1
    if "%attempts%" EQU "10" (
        echo TIMED OUT
        endlocal
        exit /b 1
    )
    bitsadmin /info download /verbose | find  "STATE: ERROR"  >nul 2>&1 && endlocal &&  bitsadmin /cancel download && echo SOME KIND OF ERROR && exit /b 2
    bitsadmin /info download /verbose | find  "STATE: SUSPENDED" >nul 2>&1 && endlocal &&  bitsadmin /cancel download &&echo FILE WAS NOT ADDED && exit /b 3
    bitsadmin /info download /verbose | find  "STATE: TRANSIENT_ERROR" >nul 2>&1 && endlocal &&  bitsadmin /cancel download &&echo TRANSIENT ERROR && exit /b 4
    bitsadmin /info download /verbose | find  "STATE: TRANSFERRED" >nul 2>&1 && goto :finishing 
    
   w32tm /stripchart /computer:localhost /period:1 /dataonly /samples:%timeout%  >nul 2>&1
    goto :repeat
    :finishing 
    bitsadmin /complete download >nul
    echo download finished
    endlocal
   goto :eof
   
   :help
   echo %~n0 url file [timeout]
   echo.
   echo  url - the source for download
   echo  file - file name in local directory where the file will be stored
   echo  timeout - number in seconds between each check if download is complete (attempts are 10)
   echo.
   goto :eof
You can check also this jscript.net self compiled hybrid (save it as .bat):
@if (@X)==(@Y) @end /****** jscript comment ******
@echo off
::::::::::::::::::::::::::::::::::::
:::       compile the script    ::::
::::::::::::::::::::::::::::::::::::
setlocal
if exist simpledownloader.exe goto :skip_compilation
set "frm=%SystemRoot%\Microsoft.NET\Framework\"
:: searching the latest installed .net framework
for /f "tokens=* delims=" %%v in ('dir /b /s /a:d /o:-n "%SystemRoot%\Microsoft.NET\Framework\v*"') do (
    if exist "%%v\jsc.exe" (
        rem :: the javascript.net compiler
        set "jsc=%%~dpsnfxv\jsc.exe"
        goto :break_loop
    )
)
echo jsc.exe not found && exit /b 0
:break_loop
call %jsc% /nologo /out:"simpledownloader.exe" "%~dpsfnx0"
::::::::::::::::::::::::::::::::::::
:::       end of compilation    ::::
::::::::::::::::::::::::::::::::::::
:skip_compilation
:: download the file
::
::::::::::
 simpledownloader.exe "%~1" "%~2"
::::::::
::
exit /b 0
****** end of jscript comment ******/
import System;
var arguments:String[] = Environment.GetCommandLineArgs();
var webClient:System.Net.WebClient = new System.Net.WebClient();
print("Downloading " + arguments[1] + " to " + arguments[2]);
try {
    webClient.DownloadFile(arguments[1], arguments[2]);
} catch (e) {
        Console.BackgroundColor = ConsoleColor.Green;
        Console.ForegroundColor = ConsoleColor.Red;
        Console.WriteLine("\n\nProblem with downloading " + arguments[1] + " to " + arguments[2] + "Check if the internet address is valid");
        Console.ResetColor();
        Environment.Exit(5);
}