How do you stop the bike? In the saddle? Maybe if you practice standing briefly as you pedal, the starting and stopping out of the saddle will feel more natural. Remember, the bike will be more stable the more weight you put on the pedals rather than on the saddle. Try putting one foot on the pedal as you straddle the bike and pushing on the ground with the other foot like you're riding a scooter. That's the starting motion.