You can certainly do your running while bulking, just get the proper nutrition, and enough of it.
People that have problems gaining are generally not getting the proper nutrition. Hard gainers just need to eat more to gain bulk, since their metabolism is burning off more calories. I'm not going to get into specifics here, and am oversimplifying, but if you take in more calories than you burn, you will gain weight. As long as those calories aren't junk, and you workout enough, it won't be bad weight.
I've seen enough hard gainers complain about not gaining mass, and looked at their food journal, they just aren't eating near enough to gain mass. I know a couple people that are fit, not huge or really muscular, that are hard gainers, and have to eat more than 4500 cals a day just to maintain their weight, and when they want to gain, they have to take in 5500+ a day to make up for extra calories burned during weight training and to have enough calories extra to gain. Not just any calories of course, they watch the % of types of food also(fat cals, carb cals, and protein cals)
If you want to get more info on how to eat to gain while still doing your cardio, talk to a registered dietitian. Also would be good to get an idea of how many calories you burn on a regular day to be able to calculate how many calories you need to take in to gain.