when I first took my resting pulse I'd take a stethoscope to bed but it would blow my eardrums rustling on the bed covers.
best way I found was to take my pulse at my wrist before I moved a muscle. 15 seconds x 4 gives a very good accuracy.
Any movement after waking sends your heart rate soaring for a few moments.You want to try sample before that happens
As Hubbub says a higher than normal RHR is a very good indicator of illness or over -training etc