Bunny shampoo is just a marketing ploy to get you to buy un-necessary stuff for your bunny. A mild pet shampoo would be fine- or even no shampoo at all. I have had to give a few butt baths and I used warm water only. Cotton hated the bath, but needed to be cleaned, and I am glad that I did not use shampoo as that only would have extended the bath/rinse time necessary.
There are a lot of companies out there that are making pet products that don’t have a clue! I HATE, HATE, HATE that there are so many products- such as vitamins and treats that are labeled for rabbits AND guinea pigs- just because they are small pets about the same size they get lumped together marketing wise. And guinea pigs and bunnies have some quite different dietary needs. They do the same with hamsters/gerbils. Companies don’t care that they are from different areas of the world and different habitats- they lump them together by size! 
Typical pet store, in my opinion- 90% of the bunnies supplies are garbage- either un-necessary, too sugary (treats)/not healthy, worthless (small litterboxes), too expensive (wood pellet litter compared to wood stove pellets), inappropriate (small bunny cages), etc….
Companies make this stuff because people will buy it- but people buy it because that is what is available and cost-effective to them.
Gee- and you thought you were just asking about bunny shampoo- and I go off on a pet store tirade. Sorry! But really, you asked a great question and the answer is to trust yourself and your research more than the companies products for your pet!