Up till just recently, my only measurements of HR were from my bike's monitor, before, during, and after riding; but that "before" starting number was always after a good 6-8 cups of coffee and a lot of morning activity; though not exercise level activity. However, doc wanted to take me off the diuretic part of the blood pressure meds as between the heat and my activity level, it was probably doing more harm than good; but asked me to monitor my BP over a month or so to see how it goes. Well, I take the measurement, BP is fine, then it spits out a pulse number of 54. This is after waking, but before caffeine and kitchen scouring routine. My normal hop-on-the-bike rate is about 82. (measured/tested max is 180).

Is that spread from 54 -> 82 unreasonably weird?

It doesn't sound too abnormal. Presumably you're taking your resting HR while sitting down and testing your BP and your before ride HR while standing up at the bike after you've been getting ready to ride.

My resting HR is low to mid 40's but when I hop on the bike it can be between 60-80 depending on what I've been doing before getting on the bike.

^^This.

You would get more out of the caffeine if you drank a lot less coffee. The effect goes down with quantity. Before a major ride, I'll sometimes refrain entirely for a few days so I get a larger effect when I do use it.

While you're certainly correct about the caffeine; with the amount I drink, it does almost nothing (relatively); I have a general superstitious belief that coffee is the raw material for code, the more coffee you drink, the more code you produce. :-D

This is true.