Below is a small function for achieving this. The search string is the first argument and the rest are the array elements:

containsElement () {

  local e

  for e in "${@:2}"; do [[ "$e" == "$1" ]] && return 0; done

  return 1

} 

A test run of that function could look like:

$ array=("something to search for" "a string" "test2000")

$ containsElement "a string" "${array[@]}"

$ echo $?

0

$ containsElement "blaha" "${array[@]}"

$ echo $?

1