If your bill seems abnormally high you might want to have someone out to verify that the heat pump is actually functioning in the first place. Otherwise, your system may be running off exclusively auxiliary heat. I had this issue when my heat pump compressor failed. The house held temperature just fine, but it was using ONLY the electric aux. The heat pump itself was physically unable to provide any warmth, despite the outdoor unit trying to run, cycling its fan, etc.
If you have a new system (mentioned in post) - depending on locality - they may have required an "outdoor air temperature sensor"...this would create a temperature point at which the heat pump portion is not allowed to run - so it forces the auxiliary (ie heat strips - aka big ass toaster in your attic) to come on for heat.
I just got a new system and was displeased to learn that the presence of such a device is a code requirement in order for them to close out the permits required to install a new system. On top of that, my inspector in particular INSISTED it had to be set at 40 degress. Meaning - if its below 40 outside, the heat pump isn't allowed to run and all heat comes from the extraordinarily inefficient heat strips. The government logic is that it prevents wear and tear on the heat pump from cycling, keeps houses at temperature, and 'helps' the consumer instead of 'inefficiently running the heat pump constantly'.
In my opinion - their logic is flawed. Heat strips are a 1:1 efficiency, while a heat pump is approx 3-4:1 depending on the outdoor temperature. The efficiency approaches 1:1 as it gets colder. Generally, I saw anything from 32F to 0F quoted as the crossover point. The general trend I found online (confirmed by a friend who does commercial HVAC design for a living) is that the heat pump will still be more efficient MUCH lower than 40F...typically 20F or lower - its still more efficient to run the heat pump. It might take a bit longer - but if youre willing to trade some comfort for savings - even at 20 degrees F the heatpump is still probably 1.5:1 or something of that sort. I adjusted my OAT override to 25 degrees instead. Frankly - it seems insane to put in a new / system that is rated way more efficient than the old - and prevent it from working in most of our "heating" months in this state. My first electric bill on the new efficient system in winter was HIGHER than almost any I had in the past when the old system was correctly working.
So the point in my whole rant? you mentioned you had a newer system - and its possible it was installed with a similar override setup. My HVAC install company, myself, my hvac friend, and every resource I found all agreed that the temp sensor if present, should be set far lower than the local inspector insisted it should be at. You may want to look into that.
FWIW, I have a ~10 yr old home and 3.5 BTU system. My past electric bills (when the old system functioned) were about $150-250 in the colder months. I hit $400 running on ONLY electric strips when that system died back in december. My new bills were $200-220 with the colder than usual weather and override at 40. I since reduced that - but have not gotten a bill to compare - my feeling is I should have seen 150-180 instead of the 200-220. If heat pump with aux electric is your ONLY heat source - expect those types of bills. Worth mentioning - I run my heat higher than most 70-72 set point.
Hope this helps - any questions ask away. I learned way more about HVAC than I ever cared to know when I needed my system replaced. I think I'd rather deal with used car salesman daily than try to replace another hvac system...