How to set rsync speed limit from eating all bandwidth with --bwlimit option

Originally published at: https://www.cyberciti.biz/faq/how-to-set-keep-rsync-from-using-all-your-bandwidth-on-linux-unix/

The rsync command is eating all my bandwidth from a backup script and generating tons of I/O. How do I set a limit for file transfer speed of rsync command on Linux or Unix-like system? How can I keep my rsync script from using all of my bandwidth?