Can a child who is younger than sixteen, and who is below an age at which they could hold a driver's license, be ticketed for exceeding the posted speed limit on a road on a (non-motorized) bicycle?
It depends on the laws of the jurisdiction. In Washington, speed limits are implemented via Chapter 46.61 RCW, the very first section of which states:
The provisions of this chapter relating to the operation of vehicles refer exclusively to the operation of vehicles upon highways except: (1) Where a different place is specifically referred to in a given section. (2) The provisions of RCW 46.52.010 through 46.52.090, 46.61.500 through 46.61.525, and 46.61.5249 shall apply upon highways and elsewhere throughout the state
We then turn to the question of what a "vehicle" is (this is the discussion of a number of legal treatises). Title 46 is about motor vehicles, but still you should look at the definition, if any, of "vehicle". We have two definitions of vehicle in RCW 46.04.670. Definition 1 says that
"Vehicle" includes every device capable of being moved upon a public highway and in, upon, or by which any persons or property is or may be transported or drawn upon a public highway, including bicycles
Definition 2 omits the italicized bicycle inclusion, and explicitly excludes
A bicycle, for the purposes of chapter 46.12, 46.16A, or 46.70 RCW, or for RCW 82.12.045((.))
This is a bit of a mess arising from legislative screwup, which should be resolved by appeal to RCW 1.12.025. The explicit-exclusion sections are about registration, dealers and taxes, and not speed limits. The latter version was recently reaffirmed effective July 23, 2023.
The courts could therefore be somewhat inclined to not apply speed limits to bicycles, because bicycles were recently removed from the set of explicit vehicles. But as notes in the Eskridge's extensive discussion of a hypothetical ban on vehicles in Lafayette Park, there are multiple principles for interpreting laws, and "legislative intent to assure safety" would be one prominent consideration, in case the wording of the law is not crystal clear – as it is not, in this case.