In your template overrides style sheet use "visibility : hidden" in the "@media size sections"
eg
@media (max-width: 480px) and (min-width: 320px) {
#expagesBarHeader { visibility: hidden; }
}
You will hide the bar but have a hole in the display so may need to add "height: 0em;"

environment Test: Zen Cart 157; Apache 2.4.46; PHP 7.3.21; MySQL 5.7.31; Linux 4.15.0