How do I capture a MySQL result set in a bash array?

With the --batch option, mysql should output the result one record on a line, and columns separated by tabs. You can read the lines to an array with Bash's mapfile and process substitution, or command substitution and array assignment:

mapfile results  < <( mysql --batch ... < query.sql )

or

set -f        # disable globbing
IFS=$'\n'     # set field separator to NL (only)
results=( $(mysql --batch ... ) )

(Note that IFS stays modified and globbing disabled after this.)

Then, if you want to split the columns of a row to some variables:

IFS=$'\t' read -r col1 col2 col2 ... <<< "${results[0]}"

---

Your assignment

linesIN=`cat /tmp/query.csv | sed 's/\t/,/g'`

is not an array assignment (it's missing the parenthesis). It just assigns the output of the command substitution to a regular string variable. (Any newlines will be embedded there, but it'll still be a single string.) ${#linesIN[@]} still works since in Bash/ksh single-element arrays and scalar variables act the same.

Another way to do it would be to pipe the output of the command to a while loop. Note you want to include the -N or the results include the column name.

#!/bin/bash
#Script to read output from a mysql command line by line 

mysql -uroot -p example -N -e "select column from table" | while IFS= read -r loop
do
    echo "$loop"
done 

And if you just want a count, you'd do a select count(columnName) and print out the results.