Try the run.exe command of cygwin. It is a big install, a complete unix environment for your Windows machine. Suppose you installed it at c:\cygwin\.
No mystery, just run c:\cygwin\bin\run.exe <your command here> and you will have your no dos window execution.
You can run it from any DOS window (run cmd.exe from the start menu). You don’t need to run it from cygwin.
To make it easier, append C:\cygwin\bin to your %PATH% env var (My Computer → Properties → Advanced → Environment Variables) (Kudos to Felipe Alvarez comment).
Now you can just type
c:\cygwin\bin\run.exe "C:\foo.bsh"
You must create a link in your Start Menu with this command so will be able to run it with Win-R.
Here is the man page of the runcommand:
$ man run
RUN(1) run 1.3.0 RUN(1)
NAME
run - start programs with hidden console window
SYNOPSIS
run [ -p path ] command [ -wait ] arguments
runcommand [ -p path ] [ -wait ] arguments
DESCRIPTION
Windows programs are either GUI programs or console programs. When
started console programs will either attach to an existing console
or create a new one. GUI programs can never attach to an exiting con‐
sole. There is no way to attach to an existing console but hide it if
started as GUI program.
run will do this for you. It works as intermediate and starts a pro‐
gram but makes the console window hidden.
With -p path you can add path to the PATH environment variable.
Issuing -wait as first program argument will make run wait for program
completition, otherwise it returns immediately.
The second variant is for creating wrappers. If the executable is
named runcommand (eg runemacs), run will try to start the program (eg
emacs).
EXAMPLES
run -p /usr/X11R6/bin xterm
run emacs -wait
runemacs -wait
run make -wait
AUTHORS
Charles S. Wilson
Harold L Hunt II
Jehan Bing
Alexander Gottwald
Version 1.3.0 November 2005 RUN(1)