I'd like to add a few comments to what Gerri said. You bolus to cover your dietary glucose load, and protein is also important (fat is essentially "free"). Dr. B says to increase protein to gain weight. Since more than half of protein is converted to blood sugar, many people find that they also need to account for that in their bolus calculations. In fact, some Dr. B followers prefer R since it acts slower and matches the glucose load better.
And while Dr. B has his recommended diet, he actually advocates a "holistic" treatment and provides a wide range of advice. He basically invented home testing of blood sugar and the basal-bolus regime. And he has something to suggest for almost everything diabetic, including lows.
Being on only a basal, it appears that your basal settings are higher than your actual basal needs and thus you need to eat to feed your insulin. That is not what you want. With such a regime, you will continue to go low if you don't eat on schedule (and eat enough carbs).
In general (for a properly established insulin regime), a low of 69 should be treated, but it should be treated with the minimum glucose needed to restore normal blood sugar (83 mg/dl). That is "not" a fatty pillsbury biscuit. I rise 2-3 mg/dl for every gram of carb I eat, you probably rise 5-10 mg/dl. Thus to rise from 69 mg/dl to 83 mg/dl (15 mg/dl rise), you need 1.5-3g of carbs. A good way to treat, smarties. Each roll is 6 grams of pure dextrose and contains 15 tablets (0.4 grams each), thus you would eat 4-7 smartie pills.
I've never met a doctor or endo who accepted my diet, and instead, I just say I am following a low carb or carb restricted diet and decline to offer further information. I have more important things to discuss at my appointments than my disagreements with doctors on nutrition and exercise.
As to your insulin regime, I have to caution you, without changing your insulin regime to match you actual basal needs and dietary carbs, you are going to experience lows and will need to treat. I would not attempt Dr. B's diet without first gaining control of your insulin regime.