# Basic syntax:
YOUR_VAR=( $YOUR_VAR ) # convert the string to an array
echo ${#YOUR_VAR[*]} # use the standard bash syntax to get the length of arrays

# Example usage:
YOUR_VAR='some string with words'
YOUR_VAR=( $YOUR_VAR )
echo ${#YOUR_VAR[*]}
--> 4

# Note, to convert the array back to a string, use:
YOUR_VAR="${YOUR_VAR[*]}"