When you say you want to lose body fat and then in the same sentence say you want to bulk up those are two conflicting goals as least the way I see it. Bulking up means to gain both fat and muscle. And that can't be done while you are trying to lose fat.
Assuming you meant you'd like to gain muscle and lose fat I would suggest a program where you rest very little between sets and you could even use the super set method. This is where you are working opposing muscle groups with no rest in between. For example, you perform a barbell curl and then without rest perform a lying barbell tricep extension. Then rest no more than say one minute and repeat.
Aside from using super sets you could simply cut back your normal rest between regular sets to no more than :45 to 1:00. Naturally you will not move as heavy a weight without as much rest but you will burn more fat.
There are actually so many other things that you can do as well if you want to train more than three days per week. Lift heavy for three days per week with normal rest periods in between sets. Then on two of your off days you can do interval cardio training. For example, sprint for :30 and rest for :30. Do 8 to 10 intervals in this manner. If you are out of shape sprint :30 and rest 1:00 this is called a two to one rest period. If you need more rest sprint for :30 and rest for 1:30 this is a three to one rest period. Then as you get in better shape you can decrease your rest time.
The above plan will give you 3 weight training days, two cardio days and two days of rest.
There are many ways to slice this cake. I have simply given you a few ideas on how it can be done. There are many, many more.