I used fully upgraded and enchanted heirlooms; missing only the fishing ring. Leveling from 1-20 took ~3 hours, at which point I immediately turned on War Mode for the duration. I rarely encountered enemy players, and when I did they almost always left me alone. But the few times I did get ganked, the total cost in time was insignificant. Maybe a total of 5 deaths from ganks in the entire 40 hours.
If you want to spend as little time on your alt as possible - just do Legion Invasions. You can use sites like (https://wow.gameinfo.io/invasions) to track when the next invasion will be. Log in, fly to the closest world quest, and once there - right-click on the quest's name in your quest log and "Find Group". Sign up for some group, or if there's none - just start your own immediately, and people will come to you. It is 10 times faster to do invasion quests in a group. Once that particular quest is complete - leave the group, and fly to the next one, where you should find another group. Don't expect the group from one world quest to follow you to the next. Then you simply log out until next invasion. You can do 1-2 invasions a day, and each invasion will give you about a level or 1.5 of experience, if you have full heirloom gear. Each invasion will take about 20 minutes.
Edit 20 It’s been a week since this post and a lot of people are still reaching out to me with questions which is fine. I have had a few different people reach out to me to help make YouTube videos based off this guide and more info in BFA which I’m more than willing to do. Whoever gets the videos up first I will link them here for you guys to enjoy.