Hi, the HR on the bike will be lower as you are not stood upright and less muscles are working.
You should nor replicate the volume of running on a bike. 10 miles running can equal 25 miles on the bike.
A hr of say 80% will mean that you have to cycle at around 85-90% of MHR.
As you are a runner not a cyclist I would reccomend you cycle 4-5 times per week
Do 2 x 60 mins at a hr around 70-80%
D0 1 x 20-25 mins at race pace
Do 1-2 x 30-45 mins easy
This will allow you to maintain some fo your excellent fitness. The problem will be this is non-specific but you will be strengthening the cardiac muscle and muscles you do mot use for running. I would do aqua jogging as this is non-weight bearing and specific to running.