I think "bonding energy" or "energy required to create a bond" is a very unhelpful concept. Although it is useful to accurately keep track of energy balances in chemical reactions, it is not a good description of what is "really" going on.
$\rm{CH}_4$ has more energy than $\rm{CO}_2$ in the same way that a pyramid balanced upside down on its tip has more energy than a pyramid lying on a flat face. Let's say there is a thin rod bracing the pyramid while it is balanced on the tip, so it is "stable." If a marble comes in and knocks over the rod, the pyramid will fall, and the rod and marble will get knocked across the table by the energy that is released by the pyramid falling.
Or again, let's envision a mouse trap, armed and ready to spring. The spring is in an energized state, held in place by a little latch. But it can't do anything unless that latch is moved. Then if a marble falls on the trigger, the mouse trap will snap shut, and will jump up and bounce around and knock the marble across the room from the energy of the spring releasing.
Chemical reactions happen in the same way. In these macroscopic examples, the energy to kick over the pyramid support, or the energy to trigger the latch, is the activation energy of the reaction. The kinetic energy of the marbles and the mouse trap flying around (as well as the noise and heat produced) is the heat released by the reaction, and is equal to the difference in potential energy of the pyramid between the "propped up" and "laying flat" states, or the difference between the spring being tightened and relaxed. And note that the kinetic energy released is greater than the activation energy required to set it off – this is the case for an exothermic reaction.
Likewise, in a combustion reaction, the molecules become reconfigured into a lower-potential-energy state, and that difference in energy is transferred into the kinetic energy of the molecules involved, which we see macroscopically as a rise in temperature and heat emission. I should say "molecules and photons involved" because some of the energy can be released directly as light.
There is no "bond that is formed" in the sense that it eats up energy to bond a $\rm{C}$ atom to an $\rm{H}$ atom. Rather, the two atoms become trapped together by the electric attraction between them – just like the Earth and Moon are "bound together" by gravity – and do not have enough energy to move apart. It requires an energy input to move them apart. This "hypothetical" or potential energy* that is not present, but would be needed in order to separate them, is referred to as the bonding energy.
*Note: I probably shouldn't call this "potential energy" in this case, since it is not – not in the sense that the pre-loaded mousetrap spring has potential energy. This energy is the difference between the energy the molecules have when they are bound vs. when they are free.