I am not an expert on ADHD and can not emphasize enough that what I am about to say is not easy to do in practice without addressing ADHD or any other emotional/cognitive condition. As with everything I write, I am not a professional, merely passionate. Professional counsel will always supersede anything I write.
When a child breaks down in tears when not getting their way, two emotional reactions are at play: their reaction to not getting their way and your reaction to your child's reaction. Depending on our responses we can either reduce or escalate their crying.
This is not a solely a child - parent response but applies to any relationship. Think about how you feel when upset and someone says "Stop being upset". It usually triggers anger because that person isn't really trying to understand your situation and how you feel. The same goes for our children. Purely saying things along the line of "Stop crying and get over it" generates the same reaction in our children as it does in us. Hence, more crying, more anger and less resolution.
What's happening within us when we respond with "Stop crying" is we are trying to resolve our own anxiety that is triggered by our child's negative response. We are trying to fix our own problem instead of our child's problem. The same goes for giving in to a demand because we just want the crying to stop - it's really us we are trying to make feel better.
Instead, practice calmly asking "Why are you crying?" with a true intent of listening to what your son expresses. Even if it's not coherent. I try to always practice complete engagement during this type of episode: constant eye contact, stop doing other things, physical touch (hold hand, rub shoulder, sit together). Your goal is to let your son express himself and feel understood because you may understand exactly what's happening, but he doesn't (It's probably frustrating for him to always cry when something doesn't go his way). Always lead your responses with "I understand that..." repeating what he's said. Show that you listened, that you heard him and know how he feels.
At the end of the day, the goal is to express "I know you don't like this. I understand you want to do something different. This thing has to be done/stopped so we can what needs to be done."
Source: Lost Art of Listening
Regarding the Bullying:
Bullying at school is not about him crying. It's that he's different. He is his own person and that should be celebrated, not picked on. I was bullied because I have big ears that stick out further from my head - a defining feature of "me" my wife absolutely adores.
I am so sorry that he must suffer such torment in a place he has to go. No child should have to experience that and if you haven't already do make a HUGE stink about this with the school authorities. It is their responsibility to keep the school safe and healthy for everyone.