Why do the ladies never stand to bid the guest goodnight?

It's a custom, largely ignored nowadays. Gentlemen stand, ladies remain seated.

You'll notice that they do occasionally stand, when the guest is someone of particular note or importance.

If I remember correctly, didn't Dorothy kiss Bishop Sheen's ring?

Believe it or not, it's for economic reasons. As you may recall, the men wear tuxedos and the women don fancy evening gowns. For the guys, it was no big deal- all they had to do was buy one black tux and they were set for life. For the gals, though, it was prohibitively expensive to buy a new dress for each Sunday night. Hence, several top designers of the day allowed the female panelists to borrow one of their recent creations and wear it on the show for publicity purposes. Unfortunately, there was an embarrassing incident where Arlene refused to return a gown- claiming the designer had given it to her as a gift. The designer, of course, denied it and there was big stink. Anyway, the result was from then on the designers would only give Dorothy and Arlene the top half of the dress- figuring a partial gown would be, more or less, useless to the wearer and they would return it without question. The reason the female panelists remain seated, is because they aren't wearing anything (or only slacks or underwear) from the waist down.

I wanna buy your carbon offsets.

One time- one silly time- the male panelists stood on their chairs to say goodbye to the mystery guest. The mystery guest (who the panel correnctly identified) was Wilt Chamberlain. I thought it was silly, rude and embarassing

They also all stood up for the very young nun whose line was a dentist, and for another young nun who was the headmistress of a Catholic military academy for young boys. And all four routinely stood for very elderly guests (e.g. architect Frank Lloyd Wright), as well as for war heroes (though not for Audie Murphy), clergymen, and major statesmen (e.g. Chief of Protocol & Ambassador Ms. Perle Mesta). (Surprisingly, neither lady rose for noted humanitarian/physician Dr. Tom Dooley, world-renowned for his charitable medical work in Vietnam and Laos, even though it was mentioned that he had cancer, of which he died a year later.)

Apparently, there was a period when even the male panelists remained seated (for departing male guests, anyway). I'm not sure of the season, but it appeared to be one of the earlier ones. Cesar Romero was the mystery guest (he stumped them), and no one (except John Daly, of course) stood as he bid good night to the panelists. And guest panelist Jack Paar (Tonight Show host) never stood for the departing male guests, even when Bennet Cerf had already risen to his feet.