Glad to hear that you aren't planning to give up your BP despite such a big move!
If you plan to drive you will need to get CITES paperwork ready for your BP as they are considered wildlife and you need a permit to import them to Canada and the US. This can take 3+ months so start preparing it well in advance - it's good that you're asking about this early! I recommend calling the wildlife border inspection for both the US and Canada to confirm how this process works. Even with all those preparations, I'd still have a backup plan (boarding options, delaying the trip...etc.) in case for some reason they won't let your BP through at the Canadian or Alaskan border.
Be VERY careful about temperatures during the RV drive and never leave your BP (or any of your animals!) unattended in the vehicle without AC or heating if you stop somewhere. I think RVs usually have electric outlets so it would be best to have a small tub set up with a thermostat, thermometer, and heat mat, and you should monitor temps closely daily.
Overall, given how long the trip will be and the fact that you would need to cross into Canada and then back into the US with a CITES animal, it would likely be easier (although more expensive) to ship your BP. There are reputable reptile shipping companies that will handle the process and any necessary paperwork for you but you will need someone to leave your BP with who you can trust to pack him properly for shipping when the time comes. I also recommend shipping at a time when temperatures are mild like the late spring or early fall - it's best to avoid times when it can get really hot or cold because sometimes accidents can happen, animals can get left in an area without temperature control...etc. and it's less likely that a mistake like that will be fatal when the weather is mild.