A good map makes exploring more fun, you can strike out confident that you'll be able to find your way back. In dance, mapping the music is my favorite way to structure improvisation, prevent over-dancing, and create texture and interest in a dance. It's also the backbone of how I keep track of what part of the song I am making choreography notes about, and how I find patterns in a song to use for the choreographies I make for students.
Every dancer uses a slightly different method to map a song, and every dancer hears the music slightly differently. So long as you are not hallucinating or totally mis-identifying rhythms (hey, it happens) this is a good thing! Every dancer should bring something different to the stage, bellydancers are meant to be more like a bouquet of wildflowers than identical roses.
Here is one example of music mapping, to a classical European song. I would like to tell you my maps start out this clear, but usually I listen to a song a few times to mentally block out the main sections (ie, verses), then grab a pencil and do a very scribbly version of this, where I then usually run out of room, lose count, and repeat and rewind until I am confident I have the level of detail I need. Lastly, I'll transfer my notes to a different piece of paper, more neatly and mostly to the left margin, to leave me room to write choreography notes on the right (because I'm writing in English).
Generally, I will note instrument textures, repeated phrases, places where call and responses happen, and rhythm changes. I'll also name the sections something evocative, maybe "slidey swirly bit", "fast violins", "beledi transition", "kanoon call, orchestra response", "melody A", "sounds like batman", "wind down", or "DRAMA TIME!". The names can be anything that help you keep track of where/when you are, and help you notice when a phrase or section is repeating, or repeating with a slight variation.
How detailed and what level of musicality you want to focus on depends on how you'll use the map. If I am making the map for myself to improvise to, I will assign general movement categories, characters, or energies/emotions to each section, and trust that having done the exercise of finding the smaller phrases will inform my dancing. If I am mapping to create a choreography, I will use each phase as a line, so that I can keep track of what part of the song my notes are for. You can throw in some time-stamps to help orient you and confirm where you are, especially if you intend to revisit the piece some time later. When you are up and dancing you won't be looking at the time-stamp, so they don't help when you're listening and trying to remember what to do next.
I also don't concern myself too much with the count, unless it is a tricky section and I am writing the choreography specifically for students. I don't like to occupy my brain with counting when I dance, it feels better to let the music fill me up and push all the other thoughts out of my head. Further, a count of 4 can happen almost anywhere in the music, but that special lilt of the kanoon, tremolo leading into a fellahi rhythm, or dramatic response from the orchestra will reference a much more specific spot and therefore is much more useful for cuing what part of the choreography you are in. If this was a map of a city, it would be analogous to: cross walks will happen at regular intervals and are easy to lose count of, but that big magnolia tree on the corner, or the mailbox painted in rainbows are much better indicators of when to turn.
For another example of the music turned into visual patterns, check out this fountain! Look for how the shapes and movement of the water draw attention to patterns, textures, and repeating or changing phrases in the music.