Hi Snoopy,
I'm an absolute beginner when it comes to Muay Thai (started about 3 months ago) but I've come to it from a background of about 4 years of training and racing mountain bikes, which means I have pretty good cardio fitness and leg strength. Terrible everything else though! I've found that my recovery during and after sessions is WAY better than some others who don't have great cardio and I can do a lot of the fitness exercises better, even though I lack a lot in upper body strength.
If the aim is to build cardio capacity and endurance, cycling can certainly help you do that but I suspect that if you're already reasonably fit, 3x30min sessions a week may not give you much benefit. Unfortunately cycling tends to be a less time efficient form of exercise than running, the trade off being that you're (probably) less likely to get an overuse injury. And going fast is more fun :) I find that unless I'm doing some kind of awful hills / intervals thing, I don't get much out of any sessions less than an hour. Seeing as you're already doing HIIT stuff, maybe think about throwing in a longer ride on the weekend?
I have wondered if there's more to the running for Muay Thai training thing than just cardio and mental toughness, though. Muay Thai involves lots of time on your feet and using your legs to generate power and perhaps running helps with those aspects too.
