Fit is key, but a part of good, easy position on the bike is the right saddle. I found that switching to one that supported my sit bones with a hole to take the pressure off the sensitive parts helped- I was putting too much wieght on my hands to keep it off the crotch. Also, if you're using a MT or hybrid tilting the brake levers up or down to give you a straighter, more relaxed wrist can make a big difference.
Third, Rapid Fire vs. Grip Shift. Depending on how you're put together, either of these can strain your hands, wrists, and forearms all the way up to the shoulder. Road bike gear has similar equipment adjustments and design differences. A good, no, look for a gifted mechanic- they should know about this stuff.
My bikes fit me beautifully off the rack, but the little tweaks and a better saddle solved the upper body problems. Hitting the carpert end doing crunches can fix a lot cheap and easy too- Ab strength holds up your upper body and gets the weight on your butt where it belongs.
These were the things that worked for me. Get refit first, then if the problem persists these are some things to look at. Hope it helps.

missliz

Handlebars were already mentioned, I think, and boy can they make a big difference.