Genetics do help, but training is huge.
It took me YEARS to get my 5k from 21ish to 18ish. I didn't make the breakthrough (15 year plateau) until I ran nearly 80-90 miles per week, or over 12-15 miles per day at peak. That's big time training.
Unlike you though, I hopped on a bike and was immediately riding 22mph and hanging with Cat4-5 roadies. On my very first try. But despite this fast nature, it took a fair amount of training to crank it up another notch, and I'm not cycling anywhere near what I should be in terms of volume.
In my experience, running gives you a huge aerobic base, but doesn't necessariliy give you the leg power to ride fast or climb hard. I was lucky in that I have natural leg power - my quads and glutes are naturally big, AND I built power as a teenager through basketball and soccer. But that probably costs me in running, where small legs and small quads are much more advantageous for distance running.
I still think that for non-pro racers, training trumps all. All the way up to the top amateur levels. It may take you 7-10 years of highly disciplined training to get there, but it's doable. Going pro though, is a whole different matter, and you definitely need genetics AND training to be in that playing field.