My parents were raised in the rural south, and though they never had bedbugs, when we were little, at bedtime, my dad would say, “Night night, sleep tight, don’t let the bedbugs bite”. Thankfully, we had no idea what a bedbug was.
The "sleep tight" part, comes from when there were no bed springs and instead, ropes, which had to be retied tied, often every day, when a bed was made, is what kept the mattresses from sagging...though I have heard that there is a different explanation of the word "tight" in this 100s of years old little good night wish. :-)
Like you, I had no idea what a bedbugs was back then either.