In my experience, Campylobacter grew best on blood-enriched nutrient media. Muller Hinton's medium showed good results, but with the obligatory addition of defibrinated blood. A good option is to use a broth for the initial accumulation of bacteria (for example, Campylobacter Enrichment Broth (Bolton Broth)), and then transfer to the agar of your choice, but with the addition of blood. In the laboratory, we most often use Mueller Hinton blood agar.
Complete anaerobic state is not required, microaerophilic conditions are necessary. To achieve them, use special "gas bags" (we use Anaerocul C, Merck and anaerobic jar) or incubate in a co2 incubator, adjusting the co2 concentration at 10%. We incubate under the following conditions: 37 C for 48 hours. Sometimes growth may appear after 24 hours. If you use Anaerocul C, make sure that the anaerobic jar is of the appropriate volume (1 bags is designed for a certain volume of anaerobic jar in liters).