I used to bulk then cut. But during the rugby/football season at uni it was impossible to eat enough and build muscle whilst trying to maintain fitness. During summer, I didn't want to bulk because I'd look fat for beach and what not. So I just do both at the same time by clean bulking.
You've just got to work out your diet before you start. You can lose fat and gain muscle at the same time, it just means that you've got to only eat the carbohydrates that you need (for energy/going to gym). Eat protein like a mad man and you'll have what you need to gain the muscle and the carb 'deficit' will help lose the fat.
It's not that hard once you get into it.
I started out my first year at uni at 100kg, 14% BF (6'4") and at the end of year two I'm 115kg 10%. It can be done, it just takes commitment.
(It's a slow process though. Gaining muscle is as normal if you're training and eating enough protein. But the fat loss will take longer because you do need to eat a fair amount to build that muscle. Bodybuilding/dieting is usually about extremes. But I don't see why people can't do both. It just takes a lot of dedication and strictness).