This has been primarily about uninsured motorist coverage, but an often overlooked coverage in bicycle accidents is PIP (personal injury protection). For those in no-fault states (FL is one) your auto policy will pay your medical expenses in a vehicle / bicycle accident up to a threshold (which varies by state.) The other drivers liability responds after meeting certain criteria.
Some of the earlier confusion stems from applying auto coverage to a bicycle. PIP and UIM protects you and applies when 'either' party is driving an automobile. As some of you have pointed out, uninsured / underinsured coverage is only written up to your liability limit which may not be enough. The solution is to find an insurer who writes an umbrella policy that is excess over your uninsured / underinsured auto coverage. You pay a lot of money to protect the other guy. Why not protect yourself?
For you bicycle purists who don't own cars, a "non-owner" auto policy is a good idea primarily for the protection it gives YOU when riding.