“tossing aside his outer garment.” This is an indication of how badly Bartimaeus wanted to be healed. The heavy outer garment was essential to stay warm and protected from the weather. It was so important to a poor person that if he needed to borrow money and gave his garment as collateral, even if he could not repay the debt, the garment had to be returned to him by nightfall, so he could use it (Deut. 24:13). But the garment was heavy and long, and if someone wanted to move quickly it could get in the way. Bartimaeus did not want anything to get in the way of his healing, and he did not want to be so slow that Jesus moved on before he could be healed. So he risked losing his valuable garment so he could get his healing, which was of much greater value to him.
“jumped to his feet.” The Greek is more literally, “jumped up,” but it is understood in the context that he jumped to his feet (cp. NIV).