Oh the bridge between a man and a woman...... Here are some thoughts as a very submissive female, on my past relationships and experiences, that might help you in your future journeys.
First, you really don't know if the lady you just broke up with is submissive or not. I myself have always been deeply submissive in my sexuality, but I am not submissive with every man I have met or even dated and in one case married (!!) - it has to be bought out by the man's dominance. I will be polite, show deference for his feelings or preferences but it is not the same as being submissive. If I know I can run roughshod over a man, in time I will - I will be very self willed and even (gasp!) become a nag to get my way - why?? because I can and by then I have so little respect for the man that I almost feel contempt.
On the other hand when a man is dominant and I know he cares about me, it evokes a feeling near worship - I want to please him. I had a boss once who invoked this feeling just by his presence and we never even dated or had sex. He had this way of standing in my space and talking very firmly to me. I loved it.