As other people have mentioned, your posture can have a huge impact on your comfort on a bike.
On a sportbike (and really, the Ninja 250 isn’t really a true sportbike in this sense…but that’s a good thing for you right now), because the riding position is aggressive and leaned forward, you need to develop stronger back muscles to lift your upper body up without putting weight on the handlebars. If you just rest the weight of your upper body on your hands, you’ll not only get very uncomfortable with stiff arms and numb hands, but you also won’t be able to accurately control the motorcycle. You can’t really turn the handlebars carefully if you’re also relying on them to stay on the bike.
Again, as others have said, the key is to squeeze the crap out of the bike with your lower body, then support your upper body with your back and other core muscles, all the while keeping your arms flappy and loose, with a light and relaxed grip on the bars. A few specific things helped me a lot when I was just starting:
– Squeeze the tank between your knees. At first, really squeeze to give yourself that sense of security, that you’re not going anywhere. Eventually, you’ll realize that most of the time you’re squeezing, you aren’t at any risk to be thrown, and you’ll learn to relax most of the time.
– Squeeze your heels into the plates in your rearsets. Every sportbike has a plate above and behind each footpeg that is specifically there as a grip point for your heel. Squeezing the lower part of the bike there with your heels will add extra confidence and help you relax your upper body.