I had forgotten how tricky this can be, as recently a few friends I was helping with dances asked the same question and just had no "ear" for the music tempo or beat.
It seems best to try to listen to the "back beat" or the bass and percussion of a song. Your dance count is often hiding in there.
Otherwise, don't fret about a count, per se, and maybe just visualize yourself or another couple dancing to the song you are listening to. And then slowly count their steps in your mind. Before long, when you hear a song, you will automatically know what dance is best suited for a certain song.
Also, be prepared to have some difficulty adjusting to live music, after learning in a studio to strict tempo ballroom music. Some live bands are wonderful, others leave you kind of "cheating" between steps to get back on count and to keep things moving as smoothly as possible.