Ours goes up in the heating season too, but I don't think it's the pumps. They do draw power, but not very much - my Taco 007 draws less than an amp. Most furnace and wood stove blowers draw that much or more. I think our increase comes from spending more time indoors. More lights, more electronics, more appliances (stove is electric and we do more baking in the winter), etc.
I'll open the kimono here because I've kept close track of cost. All told I have just short of $7k into my install. That's the whole shebang, including things I would have done regardless of stove vs. furnace vs. boiler (stainless chimney liner and insulation). I got my boiler for $1700 off eBay. Yes, it's not EPA-rated but that wasn't in the cards. It also included the wood I bought - we're in a new house so I had to stock up. Four split/seasoned cords averaged $175/ea, three cords of log at $70/ea (not yet seasoned but there's some ash I may dig into in a pinch), and one cord I cut on the property early enough that it was seasoned by winter (free). So I had five cords laid down, which was less than I wanted but all I could manage in 6 months.
We're most of the way through the season now and we've burned 3.5 cords. Luckily it's been a warm winter, with plenty of 50-degree days, or we'd probably be back on oil now. In the future I'd like to have 8 cords down each winter, judging by our usage.
The house was on oil heat before we started. The rule of thumb says a fully seasoned cord is worth about 150gal of oil. So monkey-math against 8 cords would be 1200 gallons of oil, which I think is about right because our last house was a bit smaller and we filled a 250-gallon tank four times that winter. Around here oil is going for $3.90 a gallon, so that would be $4680/year for heating costs. (I said earlier it's a big, drafty house - we'll work on things like insulation and windows in future years.)
That means we'll be paid off and in the black in 2 years. No matter what you use - stove, IWB, OWB - wood is a great way to go these days if you're willing to put in the work. Keeps you healthy too. The only exception is natural gas because its price is so low - but I personally think that won't last, BECAUSE it's so cheap. Demand is going to go up for it, and they're going to be putting it into more cars and power plants. My personal opinion is that a product that largely comes from the same process as extracting oil can't go very long without moving to match the price of oil.
Thinking about it, I can't think of a better project. All the estimates say things like upgraded windows, solar, etc. have paybacks in 5-10+ years. A payback in 2 years is huge. I did not value my labor in the equation, but I believe that's a wash anyway because I needed the exercise, I enjoyed the work, and it was a family thing - everybody got involved. There are benefits there that make up for the work.