There was a a sample of ryegrass/clover hay at the county evaluation clinic that tested more than 21% protein. It was cut late in May so the ryegrass was fairly mature, but the clover and young bermuda that were mixed in kept the protein up.
For grazing purposes, you can plan on better than 20% from ryegrass, maybe up to 25% protein. Bermuda has to be really young and tender to even get close. I did see the results of a demonstration done years ago on a dairy, where they fertilized every 28 days and mowed the bermuda frequently (1/2 field was mowed close to the ground one week and the other half was mowed the following week). Protein was checked weekly. This was started in mid-July and continued into the fall. Protein started out over 20% and never got below 15% even after 6 weeks of no rain.