Raising big bass is a simple recipe with not so simple results. Start with a good food chain, add good water, good habitat and good genetics and you have the potential to grow great bass. But, your issue will revolve around the dynamics of your fish population. Be positive you have bluegill. They are the backbone of the food chain. Do as Dave suggests, too. Check your water chemistry/quality. That's a big deal, too. Since you have lots of tiny bass, stocking Florida bass from a known source makes sense only if they are large enough to eat the dominant size range of bass in the bigger lake. We have given you a good starting point. Next, set up a good record keeping system. Keep track of lengths and weights of bass you catch. Plot them on an x-y graph, and compare over time. As you remove enough small bass, you will see noticeable weight gains in remaining fish. Plus, lengths will become variable, rather than similar.
Study ways to increase productivity of the lake, and you will be able to grow more fish as you rearrange the existing population

Teach a man to grow fish...
He can teach to catch fish...