as some others have said, everyone is different, so I'd recommend you save up the spondoolies to see a degree qualified sports coach, NOT a gym coach, there is a big big difference (gym coaches can call themselves a gym coach after a one year part time course (or even a few weeks with some courses) ) I'm afraid based on experience, that the majority of gym coaches or trainers might know how to shout at people, but their understanding beyond the muscles in the arm, is limited to boxercise classes.
You, for your body type need a bit of what everyone has suggested
maybe. You may have heard of the terms ectomorpth etc applied to body building discussions. You sound possibly like an ectomorpth. Such people don't naturally build bulky muscle but are good at endurance. But whatever you are, your endurance levels are partly set by training.
Doing HIIT is a very good way for quite a lot of people to improve their endurance, and their power, it worked on me. But it takes real effort, gut busting effort, so isn't recommended for unhealthy people, or lightly trained people. You need, as someone said, to build your base fitness up. But you say you're a good runner, which is confusing, slightly, or not, as to run well, must mean you're fit already.
Running is different to cycling. If you over the years have excelled at running, and finding it easy, then unwittingly you have trained your body to be a runner, not a cyclist. I'm envious of world class triathletes like the Brownlee Brothers, they're better at all the three disciplines, than I am at just one. But they are the extreme. Most of us have to focus on one thing.
If you want to be better at cycling, then you have to push yourself as a cyclist, and probably let some running fitness slide a bit.
I'm wondering, how good is your cycling position.
That is one reason why runners can struggle to post good cycling times, if you sit like garden shed in the wind. At typical running speed 8 to 12 mph, the air resistance is much lower than cycling at 16 to 20 mph. It might also be that when on the bike, your body isn't used to higher exertion while being bent up a bit. Your stomach tends to be a bit squashed which restricts a little more, your breathing. And if you perceive yourself to be getting out of breath, you mentally slow yourself down, because we're programmed not to like being hypoxic.
To people in general, if you're having problems getting from average cyclist to good amateur speeds, there are several links in the power transmission you need to check over. When we're young we can run on almost any fuel at all, but quality fuel makes it easier. Not just for the usual reasons, but that the internal energy transfer process is far more complicated than school biology 101. There are multiple steps in the process from food in, to muscle movement, and while we can feel out of breath and assume that our lungs are the problem, that's a quirk of the human body sometimes. It's actually the efficiency of the energy transfer system that dictates our power, for most of us. And that system can become tied and sluggish, ultimately leading to diabetes in some cases. It need training, which means focus on meal quality, and timing in relation to exercise. Get the fuel right, and the training right, then any fit person should be able to cycle 20 miles in one hour, on average.
See a sports coach. one size does not fit all. Oh and heart rate also is specific to the individual, not age or size. Some have a peak of just 150 bpm others 190 bpm.