You don't FTP to that directory.
Assuming:
user feldon23
password 12d43f9g
database name foobar
home dir /home/feldon23/www/mybackup.sql
To backup the database, you telnet in and issue these 2 commands:
cd /usr/local/mysql/bin
mysqldump --opt -ufeldon23 -p12d43f9g foobar > /home/feldon23/mybackup.sql
To restore from a database backup, you telnet in and issue these 2 commands:
cd /usr/local/mysql/bin
mysql -ufeldon23 -p12d43f9g foobar < /home/feldon23/mybackup.sql
You do have FTP access to your home directory, right?