A few thoughts:

If there's a suspicion that it might be the HRM, then get on a spin cycle where you don't have to worry about crashing and see if the pulse, by feel, is correlating with the HRM. If not, your question may be answered.

Can she get her HR up to normal levels in another sport, such as running? If so, then I would think more about increasing fitness levels than a pathology, since her heart is capable of reaching a high rate.

Are there any symptoms associated with the (possibly) low heart rate while biking? They don't have to be chest pain or shortness of breath. If she's feeling like her legs are going numb, or lightheaded, then that needs to be checked out.

The Reader's Digest version of my story: I always had a low resting heart rate, in the upper 30's to low 40's. My actual max was correspondingly below my calulated max. A few years ago my resting heart rate started dropping into the low 30's and occasionally the upper 20's. My max went down to the mid 120's. I started having lightheadedness and a choking sensation with exercise. This progressed to the same symptoms with any exertion, like walking up stairs. I went to a cardiologist when I could no longer walk up stairs without getting short of breath. It took a while to diagnose, but my heart's pacemaking cells had quit. I am now the proud owner of an electronic pacemaker. I am also back to exercising as much as I want and even do triathlons.

Bottom line: If you can't easily see that it's the monitor or increased fitness then GET IT CHECKED OUT.