As others have said here the usual thing is that when the SpO2 drops the heart beats faster to get more O2 to where it is needed. At the same time you start to breath deeper and the lungs get more O2 into the blood. This then establishes a new equilibrium heart rate until the O2 demand changes again either up or down...
The thing that I notice though is that you mentioned a heart rate of 50 - 55 with your BP meter not able to give you a BP reading. In my case that is caused by an irregular heart beat confusing both the BP meter and the pulse count on the oximeter. I suggest that you look carefully at the Pleth graph on the Oximeter (google plethysmograph) to see if your heart beat is a nice even rate or if there is an odd missing pulse. When my heart is well into its Ectopic nonsense my resting 'apparent' heart rate on the Oximeter drops to the mid 50's when it usually is mid 60's. My SpO2 during wakeful resting is in the 96 to 99 range regardless of whether my heart is 'skipping' or not.
The doc tells me the Ectopic beats are nothing to worry about and is more of a nusiance than a problem, but I am finding it a bit uncomfortable so I am having some investigations done.
DISCLAIMER - I am not a doctor so seek your own professional advice in addition to whatever you read here.