There might be different opinions on this, but as I understand the top coaches in the cycling world, the HR should be stable in cycling zone 2, ie no drift, or very little drift. Partly because rides are usually longer than runs, but there are also different loading of the muscles in cycling. If you are not a trained cyclist it is easy do overdo it and end up toasted.
I have a bad experience of all this when trying to get back to running and skimo after an ancle fracture. Had a coach who used those drift tests for setting the zones for bike training since I could not run at the moment, and I ended up severely overtrained (it was not a coach here at Evoke). Almost two years after this I have still not been able to get back to my sports, so be careful and listen to your body.