I'm assuming you are going to write her. I would first introduce yourself and give her a little background about your website. At that point, she will probably remember you asking for permission about the website. This should put her at ease and kind of break the ice. I would tell her your idea of interviewing her so that fans of the site might get to know her a little better. I would also mention that you would like to generate more excitement among her fans by them being able to submit questions that you would ask her. All the questions would be submitted in a follow up letter that she could respond to. Ask her politely if she wouldn't mind taking an hour or so to answer the questions. Thank her in advance for her consideration and taking time to consider this.
If everything goes well she will write you back saying it is a great idea and she would love to participate.
Then follow up with the questions, first thanking her for agreeing to it and taking the time. Do not go overboard with the length of the interview or number of questions. You do not want to abuse her time. I would also steer clear of any personal questions, such as "do you have a boyfriend?" "How much money do you make?" etc. Stick to questions about her experiences in comedy, on Who's Line and what the future may hold in her professional life.
After she responds with the answers to the questions, follow it up with a thank you note or card telling her how well it went over on the site and how enthusiastic her fans were.
Who knows, maybe she will do a live interview after that.
Good luck!