Schnauzer bumps are an inherited skin condition and so are not specifical;ly caused by your dog's diet.
However, good quality diet and attention to cleanliness and grooming go a long way in preventing skin problems.
As it is a genetic condition, Schnauzer bumps cannot be cured, but the proper food and shampoo can help the situation. There are a number of dog foods which could alleviate the situation. You might want to look in our Schnauzermania shop at some of the Natural Dog Foods which are good for dogs with allergies and skin conditionsd. you'll also find some suitable natural shampoos there as well.
Here's what the Encyclopedia of Veterinary Medical Information has to say on Schnauzer bumps:
"Schnauzer Comedone Syndrome
This is a condition affecting Schnauzers that produces comedones, or pus filled bumps that are usually mostly on the back of affected schnauzers. This is an inherited condition that will be present throughout the dog's life if it is the problem. There is no cure but good nursing care can make this much less of a problem.
Applying benzoyl peroxide shampoos or gels can help a great deal. Usually twice weekly bathing or gel application is sufficient. Clipping the hair over the affected areas and keeping it short can help in some cases.
Application of astringents such as witch hazel has been recommended by some vets and may be beneficial as well. Some Schnauzers will respond to isotretinoin (Accutane Rx) but I think this is still a pretty expensive treatment, especially considering the need for long term use. "