This worked for me. It does exactly what you asked and nothing more (no option processing). Whether that's good or bad is an exercise for the poster :)
if [[ "$*" == *"YOURSTRING"* ]]
then
echo "YES"
else
echo "NO"
fi
This takes advantage of special handling of $*
and bash super-test [[
…]]
brackets.
EDIT: Added "" around *YOURSTRING*
for clarity