As a follow up to your help request with our Support team, I’m sharing the reply here as well.
You can run your CI on Macs on Bitrise, but the process at certain points sort of require you to have a Mac, mostly setting up code signing for iOS, which is not sure that’s possible without Xcode. That said in case you have that set up, you might do fine. Having a Mac is still very beneficial, if not essential, since it allows you to run builds locally. Without the option to verify if your builds should be working you might have a difficult time sometime down the road in the future, but that’s more related to your development pipeline than to Bitrise.