Overwrite previous output in Bash instead of appending it

Basically the same as aneeshep's answer, but uses Return (\r) rather than Backspace (\b) because we don't know if the length will always be the same, e.g. when $sek < 10.

Also, your first echo should use $sek, not hard-code 60.

Finally, note the space after the ....

#!/bin/bash
sek=60
echo "$sek Seconds Wait!"
while [ $sek -ge 1 ]
do
   echo -ne "One Moment please $sek ... \r"
   sleep 1
   sek=$[$sek-1]
done
echo
echo "ready!"

#!/bin/bash
sek=60
echo "60 Seconds Wait!"
echo -n "One Moment please "
while [ $sek -ge 1 ]
do
   echo -n "$sek" #print sek
   sleep 1
   sek=$[$sek-1] #update sek
   echo -en "\b\b\b" #'print' backtrace
done
echo
echo "ready!"

With bash you can use the special variable SECONDS.

#BASH
SECONDS=0;
while sleep .5 && ((SECONDS <= 60)); do 
    printf '\r%s: %2d' "One moment please" "$((60-SECONDS))"
done
printf '\n'