Understand the differences first
Even though legs are the main muscle group of both sports, cycling rewards power while running is more about leanness and efficiency. You will have an easier time with very long, easy rides or while climbing as a runner but going fast is where you’ll need to do some extra work.
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Do intervals and hills
The best way of improving your power and speed is interval training. It’s not enough to just ride your bike, for real results you will need to introduce some structure. You can start with short 1-minute intervals of maximum intensity you can sustain. Do 5 to 10 of them with a 1-minute rest in between. Slowly make the intervals longer up to 5 minutes but always keep it at max effort. The best way to do this is while climbing uphill.
Do some strength training
Another sure way of increasing power is lifting weights. You will do best with dynamic exercises that involve large muscle groups and natural movements. The best ones are squats, deadlifts, lunges, and variations of those. Keep the weight heavy and your repetitions below 5 per set. Anything above that would be building muscle or endurance, and that’s not your goal in the gym. Because you need to work your way to relatively heavy weight it’s best to get a coach to make sure your technique is good.
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Run less
There’s no way around it – you need to run less in order to improve your cycling. Firstly, there’s a finite amount of time in a week so if you were used to six running sessions you might have to cut that in half. And secondly, your body also has limited recovery capabilities. You should only increase the training load by 10 % a week and only till a certain point which is your maximum. But don’t worry, both sports complement each other well so you won’t be sacrificing too much running speed if you do it right.
Give it time
If you do go for that triathlon, chances are that people will be flying past you on the bike. But if you persevere and train right, next year their advantage will shrink. And you running efficiency will still carry you well in the last leg of the race where everyone crashes and burns out most often. But maybe, more importantly, as you get better at cycling you’ll start to enjoy it much more, discover new places and friends, and become a more balanced and resilient athlete.