You don't need carbs "so your sugars don't go low". You can bulk up on a low carb diet well enough provided you get enough calories. The problem with high protein high fat diets for bodybuilders though is that it also has to be high calorie (ie over your daily expenditure of calories) so that means very high protein and/or very high fat. High protein has been associated with kidney damage in those prone to kidney damage like diabetics. High fat also causes insulin resistance so you will have to use a lot more insulin while on that kind of diet.
My advice would be to eat carbs but keep them to very slow releasing sources such as berries, plums, strawberries and legumes.
I currently eat 250g carbs a day but only over two meals which limits me to two possible blood sugar spikes throughout the day and my basal keeps me 4-5 throughout the rest of the day.