I have already added this code, as suggested by @tristup in a closed forum.
.wpcf7 form.init .wpcf7-response-output {
display: none;
}
This successfully hides the yellow bar (after about 5 seconds), but the yellow bar re-appears for about 5 or 7 seconds between hitting the send button and receiving the success notification.
Are there any workarounds for this?