How does an American Bullfrog gain energy for their growth?

They gain energy through respiration.

Explanation:

American Bullfrogs, are predators that have high energy requirements for growth and locomotion, and as they do not produce their own energy-rich food, and they consume primary consumers (birds, fish, rodents, etc.) they are secondary consumers.

Consumers are heterotrophs; they eat or consume organic matter (lipids, sugars, proteins, etc.) made for their energy intake by autotrophs. Autotrophs include plants, microbes, and other species that photosynthesize, while animals, like bullfrogs are heterotrophs.  

Heterotrophs derive energy through respiring. They burn fuel in mitochondria- high energy ATP is derived from breaking apart the chemical bonds within carbohydrates like glucose. Like all large animals, they carry out aerobic respiration:  

  C6H12O6+ 6 O2 → 6 CO2 + 6 H2O + ≅38 ATP

   glucose+ oxygen →  carbon dioxide+ water+ energy

not only is it colder, it also becomes darker, less salty, and more dense.