When it comes to relationships, sometimes the simple things matter the most. I think a woman hitting a man up shows she has some level of desire towards him, which is what all men want to field. Nobody ever wants to feel like they are doing all the work.
Not to beat on an old drum, I know if I was with a woman who never hit me up, just to even say hi or anything and only responded when I hit her up, I'd get the impression that she wasn't very interested in me. One thing a man wants to feel when dealing with a woman is that she's really into him... not so much to the extent to where she feels like she's hovering in the stalker territory, but it feels great when a woman you're dealing with just hits you up at some unexpected time telling you she is thinking about you.
Since you are coming from the perspective of a woman, I know that you feel the man should initiate the majority of times, and that is true, but if you stay with that attitude, you'll miss out on a lot of great opportunities.As long as you aren't thirsty in your initiations, you should be more than fine.