Each time I get on the dance floor to do a tango vals, I feel grateful that I was a musician for several decades before learning to dance. Timing in music is something I feel and do not have to count. When I started teaching dance, I found it hard to describe how to move to music: couldn't everyone hear what I heard?
The truth is, many people struggle with finding the beat for dancing. I recently fielded a request about how to be more musical with tango. I replied to that person, and then realized that this advice might be useful to more folks.
After teaching dance for 22 years, there are only a few things that I've found work for learning to hear and use the music:
1. Start listening to the music as much as possible; around the home; in the car; at the office, etc. Even if you are not paying close attention, your brain hears the music and starts processing it better, even without moving to it. Eventually, when you move to the music, you will REALLY move to the music because of these hours of extra "listening." This is purely aural learning, but it helps.
2. In classes, dances and practicas, watch the people who look like they are moving nicely with the music . . . and copy them shamelessly. I'd suggest getting behind a leader who looks like they are musical, and try to move at the same time. Again, this is a long process, but in patterning your body to theirs, you are learning to connect visually with the music.
3. OK, so far, we have aural and visual elements of learning musicality. For kinesthetic learning, my games about musicality help (see my other musicality posts). If you are in a class that is about musicality, you experience the movement with the music, connecting #1 and #2 to this body feeling. You can also do this in private lessons, and I'd be happy to set some up with you if you would like that. Another way to experience this is to have a musical person lead YOU so you can follow to the music and feel it in your body; we could also do that in a private lesson.
4. Last part of musicality that I do as another kinesthetic approach (and aural): make sounds! That's why I make people play my "silly games" about musicality while making noise. For some folks, attaching a sound to a movement helps them to remember how to move.
Different people learn different ways. I learn mostly visually and kinesthetically. I have a student who learns best by saying things while moving: sounds and noises that he then associates with the movement. I have some students who need to hear me explain things as their way to understand. Another students needs to stand and watch others try the movement, and then can do the movement. If you know how you learn best, you can streamline the process, but this will take some time--much longer than learning steps, but EVERYONE can learn this.
I disagree with people who say that musicality can be learned with a computer program :-)