My understanding of basal bolus is that the basal takes care of the liver drip and bolus takes care of the food.
There are things which affect the liver drip such as time of day, stress, exercise, alcohol. But, I thought, if you are fasting, your basal insulin should cover this.
If you find your BG drops when you are fasting, it suggests to me that your basal dose is too high: the way many set their basal is through basal testing which is effectively fasting and measuring out BG over this period.
I assume you are fine over night. The good news is that having a pump you can set a different, lower basal during the day.
When fasting for your operation might be a good idea to avoid the things which lower BG for the 24 hours beforehand: most commonly this is exercise and alcohol.