How to suppress Terminated message after killing in bash?

The short answer is that you can't. Bash always prints the status of foreground jobs. The monitoring flag only applies for background jobs, and only for interactive shells, not scripts.

see notify_of_job_status() in jobs.c.

As you say, you can redirect so standard error is pointing to /dev/null but then you miss any other error messages. You can make it temporary by doing the redirection in a subshell which runs the script. This leaves the original environment alone.

(script 2> /dev/null)

which will lose all error messages, but just from that script, not from anything else run in that shell.

You can save and restore standard error, by redirecting a new filedescriptor to point there:

exec 3>&2          # 3 is now a copy of 2
exec 2> /dev/null  # 2 now points to /dev/null
script             # run script with redirected stderr
exec 2>&3          # restore stderr to saved
exec 3>&-          # close saved version

But I wouldn't recommend this -- the only upside from the first one is that it saves a sub-shell invocation, while being more complicated and, possibly even altering the behavior of the script, if the script alters file descriptors.

EDIT:

For more appropriate answer check answer given by Mark Edgar

Solution: use SIGINT (works only in non-interactive shells)

Demo:

cat > silent.sh <<"EOF"
sleep 100 &
kill -INT $!
sleep 1
EOF

sh silent.sh

http://thread.gmane.org/gmane.comp.shells.bash.bugs/15798

Maybe detach the process from the current shell process by calling disown?

The Terminated is logged by the default signal handler of bash 3.x and 4.x. Just trap the TERM signal at the very first of child process:

#!/bin/sh

## assume script name is test.sh

foo() {
  trap 'exit 0' TERM ## here is the key
  while true; do sleep 1; done
}

echo before child
ps aux | grep 'test\.s[h]\|slee[p]'

foo &
pid=$!

sleep 1 # wait trap is done

echo before kill
ps aux | grep 'test\.s[h]\|slee[p]'

kill $pid ## no need to redirect stdin/stderr

sleep 1 # wait kill is done

echo after kill
ps aux | grep 'test\.s[h]\|slee[p]'

disown did exactly the right thing for me -- the exec 3>&2 is risky for a lot of reasons -- set +bm didn't seem to work inside a script, only at the command prompt