How to split a string on a multi-character delimiter in Bash?

Why doesn't the following Bash code work?

for i in $( echo "emmbbmmaaddsb" | split -t "mm"  )
do
    echo "$i"
done

Expected output:

e
bb
aaddsb

Since you're expecting newlines, you can simply replace all instances of mm in your string with a newline. In pure native bash:

in='emmbbmmaaddsb'
sep='mm'
printf '%s\n' "${in//$sep/$'\n'}"

If you wanted to do such a replacement on a longer input stream, you might be better off using awk, as bash's built-in string manipulation doesn't scale well to more than a few kilobytes of content. The gsub_literal shell function (backending into awk) given in BashFAQ #21 is applicable:

# Taken from http://mywiki.wooledge.org/BashFAQ/021

# usage: gsub_literal STR REP
# replaces all instances of STR with REP. reads from stdin and writes to stdout.
gsub_literal() {
  # STR cannot be empty
  [[ $1 ]] || return

  # string manip needed to escape '\'s, so awk doesn't expand '\n' and such
  awk -v str="${1//\\/\\\\}" -v rep="${2//\\/\\\\}" '
    # get the length of the search string
    BEGIN {
      len = length(str);
    }

    {
      # empty the output string
      out = "";

      # continue looping while the search string is in the line
      while (i = index($0, str)) {
        # append everything up to the search string, and the replacement string
        out = out substr($0, 1, i-1) rep;

        # remove everything up to and including the first instance of the
        # search string from the line
        $0 = substr($0, i + len);
      }

      # append whatever is left
      out = out $0;

      print out;
    }
  '
}

...used, in this context, as:

gsub_literal "mm" $'\n' <your-input-file.txt >your-output-file.txt