Since you already know the lip position for "V" is somewhere between "F" and "B" the next thing to consider is air flow.
If you are getting a POP or "B" sound then you're cutting off your air flow.
The "V" sound needs constant airflow like the "F". If you try making an exaggerated F sound then slowly draw in your lower lip. You should feel the air flow begin to make your upper teeth and lower lip vibrate.
That little vibration is exactly what you need for a good V sound.
To develop your skill at making those 3 sounds practice this word combination: "Beaver Fever"
Begin slowly, focus on the consonants and the vowels will happen naturally. "Bee-Ver Fee-Ver"
As you repeat that you should feel yourself making that transition more easily.
You may also want to think about how "V" relates to "W".
"W" relies on a very similar air vibration, but it's between your upper lip and lower lip.
Try making an exaggerated "W" sound, then slowly pull your lower lip back.
You will feel your upper lip stops vibrating but your lower lip still vibrates, when you draw it back far enough that your upper teeth vibrate then you're making a perfect "V" sound.
If you still get a "B" sound then you have accidentally drawn back both lips.
To fix this, practice this word combination: "Weaver Viewer"
Begin slowly, focus on keeping your upper lip completely still. With practice you should begin making the entire sound of both words by only moving your lower lip.