Just searching your issue on Google I read that many use an extension for it so looks like there's no option to always show BCC by default. Perhaps I suppose you're having this issue on Thunderbird, right?
You can make it visible by default by checking the "BCC these email addresses" box in account settings under "copies and folders" and leaving the box blank (delete the email that goes in there by default). (I was able to do this in TB 115 and it works in 128)