Here are a few additional comments on your code to consider:
Line 17:
Using bash version GNU bash, version 3.2.51(1)-release (x86_64-apple-darwin13) on Mac OS X, the statement: ME_DIR="${0/${0##/*/}}" gives me the error: bad substitution: no closing `}' in ${0##. This may be a bug in this version of bash, since ksh sets ME_DIR to the directory specified when your script is invoked (or an empty string if no directory was specified). There are several other ways (easier or faster or both) to get the directory from $0 depending on how ME_DIR is to be used, but since ME_DIR is never referenced after being set, the best thing to do is to just delete this line.

Line 37:
This can be more simply written as WIDTH=${COLUMNS:−$(tput cols)}

Line 38:
TOTAL is not used; delete this line.

Line 39:
This can be more simply written: ((WIDTH -= (${#BORDER_LEFT} + ${#BORDER_RIGHT} + 2)))

Lines 52, 54, 56, 73, 109, 114, 120, 135, 172:
If you change var=true and var=false to var=1 and var=0, respectively; you can then simplify if [ $var = true ] to if [ $var ]. These changes won't make a huge performance difference, but assigning one character to a variable is a little bit faster than assigning for or five characters and [ $var ] is a little faster than [ $var = string ].

Line 49:
This comment doesn't seem to be needed. If it is needed, it should appear closer to line 58.

Line 64-73:
I have no idea why you are playing all of these games with your command line arguments. If you want to know how many arguments there are, use $#. I see absolutely no reason why it wouldn't be valid to call tui-printf with two empty strings and a third non-empty string tui-print "" "" "right string" to print empty left and middle headers. To determine if $2 was given on the command line, use [ $# -ge 2 ] not [ ! -z "$2" ] (and not [ -n "$2" ] which would have been a simpler way to code that).

Line 64:
Of course ARGS=(${*}) fails to preserve argument boundaries if any of the args contain spaces. If you insist on using $ARGS instead of just using $1 though $n, you need something like ARGS=("$@").

Line 137-140:
I don't understand why you have such complex code to set adder to a single space. I would have thought you would want to set adder to a space if the length of $2 was odd, or to an empty string if the length was even. You could replace these four lines with the simpler (and probably faster):

Code:

	num=$(($#SECOND / 2 * 2))
	[ $num -ne ${#SECOND} ] && adder=' ' || adder=''

Line 155-159:
The variable len_compare is not needed here and your computation of adder is slow compared to other alternatives. Change lines 156-159 to:

Code:

	adder=$((len_strings % 2))

Note tha I also strongly suggest that you change adder to somehting else. You used adder on lines 139 and 143 to hold a string; while on lines 158, 159, and 161 you use adder to hold a number. Please use different variables for each intended use.

Line 167:
All of your calculations of string lengths are completely wrong if any operand to tui_printf contains any percent characters (%), backslash escapes (such as \n, \t, and \b), literal control characters, or non-printing characters.

If the user could ever want literal \ characters or literal % characters to be included in the printed output, you should change:

Code:

printf "${COLOR_LINE_START}${BORDER_LEFT}${COLOR_LINE_IDENT} ${FIRST}${SECOND}${THIRD} ${COLOR_LINE_CLOSE}${BORDER_RIGHT}${COLOR_LINE_END}"

to:

Code:

printf "${COLOR_LINE_START}${BORDER_LEFT}${COLOR_LINE_IDENT} %s ${COLOR_LINE_CLOSE}${BORDER_RIGHT}${COLOR_LINE_END}" \
	"$FIRST$SECOND$THIRD"