If you're eating in a calorie surplus, then you won't be able to 'shed' body fat at the same time. I would certainly include some type of cardio into your training routine to help minimize fat gain while bulking, but it will be difficult to lose body fat while eating enough food to build muscle. If you're very new to training this can be accomplished, but after 10-12 months of consistent training it is very difficult to do both at the same time.
I would focus on one goal (muscle gain or fat loss) and be sure you are eating properly to support your goals. I always incorporate HIIT during my bulks to minimize fat gain, but other than that cardio is kept to a minimum on a bulk. I typically do HIIT 2-3 times per week while bulking, and I've noticed that it can be very beneficial for staying leaner while gaining weight.