Actually, SwingLow, "wherefore" is just an archaic way of saying "why". So that's a bit of a malapropism you have going on there. You could just have said "where" and all would have been well.
I found the most effective web pattern to be vertical and horizontal cross hatching, leaving the four corners empty. Very stable that way and can take a lot of destruction without dissolving completely.
I got a bat at under 10,000 points.
A hint for those looking to get the BF Badge:
Once your tank is maxed and you've defeated the Boss, simply head away from the centre point in a straight line (in any direction) and you'll eventually hit all four of the menacing bubbles of evil.
 "Zilch"){kind=icon}
 "99 Bricks"){kind=icon}
 "Bloons Tower Defense 3"){kind=icon}
 "Duck, think outside the flock"){kind=icon}
 "Color Infection"){kind=icon}
 "The Several Journeys of Reemus: Chapter 1"){kind=icon}
 "Arachnophilia"){kind=icon}
 "Bubble Tanks 2"){kind=icon}