Can't comment on the technical aspects as I have no idea.
In which city do you live by the way?
I will tell you a thing or two about my own experiences. Even though I live in an independent house, I have many neighbours in close proximity. The ones who are a hassle are generally the ones who own their own dwellings. The folks on rent usually never bother.
First thing is that generally no matter how any neighbour puts a matter across, it will come across to you as harsh. I had a neighbour complain about my music too. Like you, I too play music whenever I am in the mood and that happens once a while and never at night.
At first, I used to get really worked up whenever a neighbour complained. Then there was this phase many years ago when more than one neighbour started complaining about all sorts of silly things such as bursting firecrackers (not crackers but the other stuff) during Diwali, trimming my creepers, putting fertilizer in my garden, etc. I finally realized that I am encouraging their behavior by listening patiently to them.
Finally I got fed up and so I started telling them that I am not going to do a thing, they can complain to whoever they want. This has worked really well and no-one complains any more.
Fact is, there are people who complain unnecessarily without rhyme or reason. The neighbour who complains about my music has a husband who plays Hindi oldies really loud. I often think about complaining but don't because I enjoy the music. Similarly, the one who complains about crackers burst crackers right in front of my house. I sometimes think, what a bunch of hypocrites these people are.
Now the other thing to note is that, sound does travel really far. Fact is even my TV can be heard on the street at times. But I generally think the one that troubles everyone is bass especially the type that shakes the windows of other people's homes. I am not sure if your bass travels all the way to the other building and rattles his windows. As for him not being able to hear anything, you may need to either move your stuff to a distant room if you have that option or spend a lot of money to sound proof your room.
A final option: Have you considered headphones? They will be a lot cheaper than soundproofing.