Your max values for cycling (both HR and VO2max) tend to be approximately 85% of what you see if you're running. That's because cycling involves slightly fewer muscles than running, and, with more resistance on the pedals, will make you accumulate lactic acid faster than if you're running.

Usually, the better cyclist you are, the closer you can get to your running maxes, but it's rare to be able to achieve a true max on a bike. Ideally, you'd do a max test running and follow it up with a max test on a stationary bike (provided the lab has a stationary bike that's got somewhat of a road bike geometry rather than an upright one) within 5-10 days of each other so you could get your true max as well as your functional capacity for your sport.

If you have a small working "window" for heartrate, then you'd benefit from lactate threshold testing (everyone can, actually). That way, you can focus some of your training sessions on pushing that level up to a higher percentage of your maximum work capacity.