Bass frequencies are long and travel through the thickest walls and for a good distance. That's why when there's a party at the other end of the road all you can hear is a kick drum. Same when people have loud music on in a closed car. Whether you're an owner or tenant makes no difference to the person you're pissing off. I'm lucky enough to be able to make as much racket as I want to during the day, but I quite often get a hankering to play bass at 2 or 3 in the morning, so it's headphones or not bother.
If you take time to get a decent sound through headphones (a decent pre helps), there's no reason not to use them. Take some powerful drugs and imagine you're doing an important take at Abbey Road or something, I don't know. But there's nothing worse than neighbour noise, I've moved a couple of times because of it.