At 9 months, your dog is still very much an adolescent and learning the rules of doggie communication. I doubt very much your dog is either "Dominant" or "bossy" - an individual dog will tend to respond to different dogs in different ways... even dogs who live together may have a more fluid heirarchy, one being the "boss" in terms of food, but giving way to another when out meeting other dogs, for example.
I have a dog who I have to monitor quite carefully with other dogs... but her reactions are generally nothing to do with "dominance".
She lacks confidence in general, and had some very bad experiences with other dogs when she was a pup. Therefore if a bouncy, in-your-face dog approaches she will tell it off. If an adolescent dog approaches, she will normally tell it off and if it moderates it's behaviour, go on to play. If a puppy approaches she is normally very tolerant, unless the pup gets too bouncy in which case it is gently put in it's place. If a polite older dog approaches she will greet appropriately, or avoid a meeting if she's not 100% certain. She will avoid larger groups of dogs, and can get very defensive if dogs hem her in. Timid dogs she is very patient with, however overly submissive dogs (those who approach confidently and then turn on their back) she will bully if I don't call her away... and there are a few dogs who she hates with a passion and will tell them off as soon as look at them, even though I cannot see how they have offended her in the slightest. So in a very few situations she can be a bit of a bully, but most of her interactions with other dogs are tainted with fear and uncertainty on her part.
The key in dog interactions isn't so much how your dog in acting, but what the other dog does and how your dog responds to that... if another dog keeps coming back for rough play, then they are both enjoying it and it is not a sign that your dog is a bully (though with adolescent dogs it can be an idea for owners to intervene and calm things down from time to time so that they don't learn bad play habits).
If another dog acts scared, or backs off from the greeting, you would expect your dog to show some calming signals (lick lips, turn head, yawn etc) or other non-threatening behaviour (a relaxed/happy lie-down, a play bow, approaching the side of the dog rather than head on or straight in for the bum-sniff).
If another dog yelps during rough play, you would expect your dog to immediately back off.
How young are the younger dogs she tends to overdo things with?? Puppies can be very rude - while adult dogs tend to give them a generous puppy license, adolescents don't always know to do this... the key is that if a puppy yelps/submits etc, your dog should then back off - if not call her away and reward her for leaving the pup alone. If it's other adolescents, I suspect it's just a case of teenage macho-ism.
Does your dog get to play with older steady dogs?? This is the ideal way to ensure she grows up with appropriate manners, as an older dog will not hesitate to tell yours when she has overstepped the bounds...
