I think you've gotten some good advice here about bathing buns. Shallow, warm water is best, as is a good rinsing. Staining can be a problem and it's doubtful that pet shampoo alone will make the stain disappear. You might try the hydrogen perioxide but be sure it gets rinsed off well. NEVER use a rubbing alcohol on fur.

Miss Emma has a bad habit of getting her fanny wet and she does get a bath every so often. She was an adult when I started this and she really seems to like it. I get bunny kisses and she likes the hair dyer too. Daisy was seriously ill about 2 years ago and then only thing that got rid of the staining was...time. It took about 2 months for the stained fur grow out. So unless it really bothers you, Heather, you may not need to give her a bath at all.