If a person has a very full bladder can it cause the person to have an orgasm? Would there be a difference for a man or a woman?
At the risk of opening the watersports floodgates, I’d hazard a guess that a woman with a full bladder is far more likely to release it during orgasm than a man. Not that that answers either of your questions 
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“Far more likely” is an understatement. I’m pretty sure that there would have to be some sort of severe equipment malfunction before any man is even capable of urinating during orgasm. I mean, for a man to orgasm, and erection is a given, and, as anyone who has suffered through the combination of a full bladder and morning wood knows, erections and urination are mutually exculsive states.
TMI WARNING
Not necessarily related to bladders or urination, but as you may be aware, nurses and doctors can jam a finger up your ass and “massage your prostate”, forcing semen out through your willie.
One time, I was taking a Massive Shit[sup]®[/sup] and apparently my prostate was naturally massaged enough, that without orgasm or any unexpected sensations, I looked down and saw massive amounts of semen dangling from my flacid member.
Then again, at that time, I remained a hormonal teenager, and blue-balls might have been the true cause.
Excellent!
I’m glad I stopped by this thread. I really wasn’t ready to call it a night without hearing someone describe how they spewed forth semen whilst taking a dump.
The Master speaks on this topic.
dont know about the original question, but releiving a very full bladder is often more pleasurable than an orgasm, as for taking a long overdue dump, wow!
FYI, no medical license is required to be a Prostate Massager!
That’s just another example of the useful information you can find every day on the Straight Dope Message Board. I’m so proud. 
Wow … okay, to get back to the OP …
I find that having a full bladder doesn’t CAUSE me to have an orgasm, but it can definitely help, especially when I’m … um … taking care of myself. Must be the extra pressure or something.
(I’m a woman btw).
Oh, and no, it doesn’t cause me to pee the bed or anything …
But it’s my understanding that men can’t ejaculate when they have to pee. Sue Johansen of Sunday Night Sex Show fame explained it but I can’t even begin to describe it.
TMI ALERT! Not true (speaking from experience). However, it causes a rather odd burning sensation sometimes when you do pee later on.
You’ve got it backwards. We can’t pee when we have to ejaculate.