I have seen that Cypress is a good bedding substrate. In the Eastern USA, this is generally true.
I am posting this because there may be readers in other countries who already know what Cypress is where they live.
Read the package label. Flip the bag of cypress over, make sure it is 100% cypress. In the USA, Cypress is the Genus Taxodium. In other countries, Cypress may be the Genus'es Juniperus, Taxus, etc. The American vernacular of "Cypress" does not always translate accurately, as the Genus Cupressus and Cupressocyparius are vernacularly called Cypress as well. As are other wholly unrelated species within the Coniferaceae.
Reading the backside of a bag labelled "Cypress Mulch" seems to often reveal that the bag contains "cypress and a blend of other hardwood mulch". Undisclosed additional species of hardwoods may cause irritation