“Hitting the wall”, or "pinging" is colloquial for having your heart rate bouncing off your Max Heart Rate (MHR). Being overly out of breath and head-dizzy are symptoms.
“Bonking” is colloquial for when your muscles run out of glucose-etc. Your entire body aching – especially your shoulders – is a symptom.
These are two very distinct feelings; but are somewhat interrelated. Sounds like you're suffering from the first. In my experience the first can start to happen more dramatically (noticeably) as you get older – “older” as in 36yo mind you : /
I had the first example above happen so bad one time in Santa Cruz that I had to get off my bike and walk. I had had plenty of food, and absolutely knew myself – I knew I wasn't bonking and couldn't understand what was happening to me – but I pushed too hard for too long to try and keep up with an amazing athlete on a hill climb. This is colloquially called “exploding”. You see it all the time in professional bike races during hard climbing events. Once you “explode” you can't recover while still providing output to the bike. This happens easier as you get older – even though you think you are at exactly the same (or better) physical condition.
A third thing is ”heat exhaustion”. This is a whole 'nother animal, and the most dangerous of the lot. I've explored the depths of these three failure points quite a few times. It's good to know where they are, but to be sure, one day you may “take it to the next level” and be completely shocked by what your body is doing,even though you think you understand what these things are...
You need a heart rate monitor, and to review the breadcrumb heart rate data for a race on your computer and see exactly what your heat is doing when you feel that way. The numbers will be clear as day. Or you can just look at your wrist/stem when riding and SEE you're “pinging” off your MHR – and if you stay there for long, you'll feel that “explosion” coming - irretrievably out of breath and often dizziness.
“That's rodeo” as far as bicycle racing (sans downhill, in most cases) – scrunching up against a predetermined heart/work rate and staying there. The way this feels, as far as work output, can vary widely – hugely in fact – depending on altitude, food, sickness and countless other things – and especially nerves – but the numbers don't lie as far as optimizing your output.
Hope that helps.
Be careful. Genetic predisposition for heart problems may onset. A full checkup may be required – even if you're only 40-some years old. People die from heat attacks in their 40s – even athletes.
EDIT: One final thought – as a runner you probably understand clearly the notion of stride length. How extending your stride just slightly can drastically increase your speed for basically the same amount of work. And like rowing, or swimming, where getting that extra “reach” - even an inch – can really make all the difference in the world for max top-speed. I see breathing as exactly the same – especially road racing. Take a big breath right now. Then take another breath and exaggerate the total input – EXPAND the lungs. THAT right there – training yourself to do that all the time when riding at your predetermined heart rate, will effectively be like having the extra few inches of “reach”.
If you ride hard enough long enough – training – you just naturally acquire it. But understanding what the desired end-state condition “looks like”, can really help you get there ..faster.
When you “explode”, as I've call it, that whole process of breathing is out of sync with your body. To try best to work through an explosion in a race is exactly – precisely – directly – the art of breathing big and consistent, even though your body is saying you really don't need to – because it's overloaded and wants to make you slow the F' down.... it's making you hyperventilate with shorter 25% quick breaths.