Probably not. Healthy gums do not bleed. If they are bleed they are unhealthy and the cause of that is ineffective toothbrushing. Plaque is being left on the teeth, which is causing inflammation. Changing to a soft brush will make your brushing less effective. It is better to carry on with a medium brush making sure that the necks of the teeth are being thoroughly cleaned. As more effective cleaning is being carried out the gum health should improve and the gums will not bleed. Scaling by the hygienist will also help.