.....your in CA? But the west coast in general
IIRC water is VERY hard with minerals, so lather for anything would be hard to come by.
How's the washing machine, and other soap related activities doing in the suds department?
If not great, might be time for water analysis, and or a softener.
If this is all wrong, consider it reductive and disregard.
Sorry if I was not clear in my response. Suds are a by-product of soap and water mixture and they have no impact on the cleaning process. They are however, a good indicator of the amount of active soap in the solution. So for instance, if one soap produces twice as much suds as another soap at the same dilution ratio, then you can assume it is twice as concentrated. Additionally, if the soap loses its suds while washing a very oily car, then you can tell that the activity of the soap is reduced since most of the surfactants have been consumed in the process of emulsifying oils in water and you might want to add more soap to the bucket or use a fresh bucket.
After reading a Car & Driver story in the 80's about auto detailing I used Ivory liquid for years as a car wash soap. The car I washed had nice shiny paint after 23 years. I did wax it regularly, of course. At some point I was informed that Ivory, like other dish washing soaps, would strip the wax. So, I went back to car washing products. None of them produce the nice lather of the Ivory. I've just learned to live with the new standard.
I should mention that I was able to reduce the waxing frequency. Ivory is pretty mild as dish washing liquids go, but probably not as mild as products made for cars.
Have been using Meguiars Gold Class, which I found to be a great product. Reasonably priced, easy to find.
However, this summer I picked up some Duragloss 901 Car Wash and I have to say I love how slick it is and the shine after washing makes it look like you just waxed your car!
Of course if you are just looking for suds then I guess you could pick up a foam cannon. I grabbed a cheap sprayer awhile ago at a HF tent sale haven't tried it yet...maybe after the winter?
Are you putting the soap in the bucket before or after the water? If you are putting the water in first, then the soap, you probably won't get much suds. Want suds?, put the soap in, then use a sprayer on the hose to fill the bucket, and every brand I have tried makes LOADS of suds