Dear student
as no external forces act on bullet and gun system so all the forces will be internal which are equal and opposite as per newtons 3rd law . if the force on bullet is towards right than reaction of that force on the gun must be on left as action and reaction acts in opposite directions . so a backward jerk will be feel
both the approach to give the answer are identicle as law of conservation of momentum for a system is a direct consequence of newtons 3rd law