[EDIT] Oops, you are asking about how to keep the SO his focus on a particular contact. Sorry, don't know and can't help. But the warship (destroyer) is likely escorting all around the target. So not weird the bearing is all over the place. However, I will leave what's below for informative purpouses anyway.
Which 4 bearing method do you use exactly? Is it the one where you keep moving in between taking the bearings? Or the one where you sit still for the first 3 bearings (or move quite slowly), and sprint away to take the 4th from a different viewpoint. With the latter method you should not be turning during the first 3 bearings. So make sure your rudder is amidship. Or make sure you add your course at the time to the reported bearing, and work with 'true bearing' instead. But there may still be rounding off errors if it is given in round degrees. If so, take a longer bearing interval. Bearings differing just a degree or so is not going to work with these methods. Make sure they differ atleast 5 degrees or more each time.
With the first method you do not have to move in a straight line, but can make wild course changes and position yourself all over the place. Or you move in a straight line and make drastic speed changes to seperate the listening spots irregularly. Infact with either method, you usually do not want steady bearings, since then the bearings will not converge. Steady bearings mean the target is very very far away (beyond the orbit of the moon
), or it is on a parallel course with same speed. Again, longer bearing intervals is the solution to figure out which case it is.