This is a very good question that I think 'ewest' should investigate for one of his Science and the Cutting Edge Pond Boss magazine articles. 'ewest' is IMO our fish bioenergetics guru. Energetics - the branch of science dealing with the properties of energy and the way in which it is redistributed in physical, chemical, or biological processes.
Read through this post from the Archives about Bass Management for some info on this topic. http://forums.pondboss.com/ubbthreads.php?ubb=showflat&Number=130299#Post130299
This is my 2 cents on this. The 10 lbs rule for bass or predator weight gain is based on the basic ecology food chain trophic pyramid where each higher trophic feeding level loses energy/biomass by a general factor of ten. Note all fish that eat other animals are a predator (aka heterotroph); even panfish that eat insects are technically predators. This is in contrast to autotrophs who manufacture their own food i.e. plants.
There is likely some variability in this 10:1 eating weight gain ratio based on numerous ecological factors. I think one of the main factors is how much energy the heterotroph (predator) needs to expend in capturing those 10 lbs of food. Having to expend excess energy capturing food would IMO increase the 10 lb:1 lb ratio for the target 1 lb weigh gain. Keep in mind that most of the biomass (weight) a predator eats is comprised of mostly water, sometimes 90% or more.
IMO the 10 lb rule is an average for all sizes of heterotroph - consumer. It stands to reason that one would need more consumables when growth is the fastest. Plus it has been shown that as fish get older the amount of food (percent of body weight) consumed per day/year decreases. This is likely due to slower overall body weight increase.
I think that ewest has covered this topic previously, but I could not locate it. He will hopefully respond. When he does, I will but this thread in the Archives for LMB Culling and Management.
So to answer your initial question of biomass needed for a bass to maintain a constant weight my best guess is about 5 lbs per year.