You don't need to ride so hard your lungs ache to get fit - in fact, doing this regularly can impact detrimentally on your fitness.

You also don't need to run to work your body aerobically.

To increase fitness on the bike, you should be doing a significant number of rides in zones 1-3 ... where you can still talk but your heart is lifted.
Do some rides in zones 3-4... where it becomes difficult to talk.
Do least rides in zone 5, 5a and 5b... where you no longer can hold a conversation and where breathing is heavy to gasping.

Aerobic fitness is about being able to use oxygen efficiently, and you can do this on the bike by lifting your heart rate a bit. I say this, because i would never choose to run, when I want to get fit for cycling, and if I can do it on a bike, then thats where I would choose to be.

However, I do acknowledge that this is my personal prefernce, and running (or other cross-training) is a legitimate way to achieve your goal also.

I guess I come from the thinking of... I want to get fit for cycling and bike-racing - why on earth would I run because running makes me fit for running, not cycling... just my 2 cents. have fun finding something that works for you.