Hi Anna
I can't explain exactly how this happens. Can you not tap your feet to a piece of music without counting? I'm sure you can. Can you pick out the first beat of a bar without counting? Well, you have to pick the first one as a starting point, so this must be possible. There are 'clues' in the music.
Try this. Go to the music store. Choose 'browse by album' and pick "the Best Vol 11"
On this disk, play the second track "greenwaves". There is no rhythm accompaniment- just a vocalist(this changes later - in fact this is a superb track). Could you not dance a slow waltz to this? And pick out the first beat of each bar. There are clues in the music itself. Its not just rustling of leaves.
Occasionally i count beats. In line figures, for some reson, and in some parts of our quickstep.