Without extensive HR/O2 monitoring, it is difficult to compare. Cycling is less aerobic than running in general but this doesn't mean you cannot get an equal workout. Any stationary bike is about as interesting as cold oatmeal. Get a real bike, it can also save you money in transportation!
To replicate running, you need to keep your effort constant but this is not easy if you have wind or hills and damn impossible with mountains unless you have the proper gearing AND a good base level of training.
Ideally, you need 3-4 sessions per week, each about 2 hours in duration. Using a HR monitor is the fastest way to determine where you need to be but in general, you should never feel winded and should be able to speak normally without gasping.
If at any time you feel winded, you are exceeding your maximum rate. Slow down. Again, a HR monitor will help you most unless you only travel on the same course etc....ignore speed. Too many variables. Focus on average speed but don't get obsessed. A bicycle is simply a machine that makes your motive power much more efficient and by doing so, small variations in your ability will be magnified greatly.
Now that is for the beginner. If you get advanced and just have to know, there are a few devices out there that measure power you are producing on a real bicycle. For the average male, producing a constant 250 Watts generally means you can do the running part of the APFT to the max.
Yes, I am the gadget guru on bicycles and have the Polar S720i with the power measuring option on the road bike. It measures chain tension by measuring the chain vibration frequency, just like an electric guitar. It also measures chain speed. Chain speed in meters per second multiplied by chain tension in Newtons is Watts of power. This system also records the power, bike speed, distance, HR and altitude (barometrically). Data overload for most but sure helps getting the most from workouts.