Carbs are set up for the flow characteristics of the carb. The Chinese carbs are copies of patented designs, but the machining is not as precise. Therefore, they look the same and bolt up the same, but they don't necessarily react the same to changes in air flow and it the flow of air that is responsible for picking up the fuel (siphons it out of the float bowl) that mixes with the air to support combustion.
The first thing to do is to use fuel the carb is designed for. The Chinese and Japanese do not have alcohol in their gasoline. Alcohol is harder to ignite and burns cooler. It takes almost twice as much alcohol mixed with the same amount of air to provide acceptable power from an IC engine. Mixing alcohol with gasoline means you need to adjust the fuel/air mixture as the alcohol displaces gasoline leaning the mixture. Normally a leaner mixture means increased combustion temperature, but alcohol burns more slowly and cooler than gasoline, so the increased temp of the lean gasoline to air mixture is offset by the cooler burn of the alcohol mixture. Using the fuel the carb is designed for may eliminate bogging at certain throttle settings as the fuel to air ratio varies.
The BST carb was engineered by Mikuni and is designed for economy - not performance. If you observe the operation of the carb closely; the slide rises in relation to the vacuum the engine creates on the engine side of the butterfly valve. The vacuum is drawn on a small port and is internally ducted to the top chamber where the reduced pressure attempts to lift the slide valve. The slide valve operation is counteracted by a spring and the weight of the slide. In theory, the slide position is dependent on engine speed, but on a single cylinder engine, the vacuum is in pulses, so at lower speeds, the slide bounces. As the slide rises it allows more air into the engine and the needle in the slide controls the amount of fuel that can mix with that air. As engine speed increases and the vacuum becomes more constant, the slide does not 'bounce' as noticeably and positions itself at a relatively constant position.
Now if the butterfly valve is opened suddenly from a constant setting, the vacuum drops and so does the slide. The slide reduces the air flow into the cylinder and likewise the amount of fuel being mixed with the air. Each intake stroke causes the slide to rise, but during the compression and exhaust cycles, the slide descends. This is the action of the Constant Velocity carburetor. Keeping the velocity constant increases the efficiency of the carb while providing acceptable acceleration performance.
Getting rid of a bog (lean condition) is difficult to engineer out of a carburetor. It is a matter of compromises. It has to be too rich at some throttle openings and too lean at other settings, but as long as the lean areas are not so lean as to cause engine damage, then the compromise is acceptable.
To get rid of a bog just off idle, it has to be too rich at idle. This is accomplished by either adjusting the fuel screw to a richer setting, raising the slide needle to enrich the entire RPM range or changing the slide needle taper which may enrich the low speed while maintaining the mixture of the original needle in the mid range. But a bog from mid-range to full throttle may require changing the speed of the rise and fall of the slide. If the slide rises too high for certain throttle settings, it may provide an over rich mixture at mid-range while going lean momentarily before the slide falls sufficiently to increase the air velocity necessary to pull fuel through the needle jet. The reaction of the slide may benefit from a stronger or longer spring.
The Mikuni VM and HSR tuning manuals are 20 pages, but I have never seen a CV tuning manual. You have to use the info in the other manuals and apply the techniques to the CV carb.
Try changing fuel first - sometimes it is a simple as switching brands. Switch from Phillips 66 to Casey's or vice versa and see how it performs. Switch from alcohol blended to pure gas or vice versa. Or tear into the carb and start changing calibrations, but only change one thing at a time in case you need to change it back.