First of all, you must know what type of bumps you have. Mostly, people complain about a boil or bacterial pocket around the piercing. These infections make the skin red and squirrel away pus or blood. Another type of bump is hypotrophic bump in which the skin becomes hard. However, it is not painful. The most dangerous bump is keloid scars as they are only removed through surgery.
If you have boils around your piercing then sea salt soaks can be really beneficial. This treatment is easy and effective as you will have to mix 1/8 teaspoon of sea salt in warm water and soak the piercing for 5-15 minutes. You will have to do it for couple of days and you will see that soaking has removed the pus from the piercing.
If bumps are severe and sea salt is not working then you can also heal these piercing bumps with chamomile tea bags. Just dip the tea bags into warm water and then provide your piercing some heat. Do it twice a day and you will see a significant difference.
Another way to heal bumps is to apply tea tree oil on the piercing. Just dilute a few drops of oil into a shot glass and then apply on the effected part of your skin. Tea tree oil is a natural agent to kill the germs. However, use it carefully as it is strong enough to make your skin dry.
If you have hypotrophic bumps then massage that part of skin with oil or topical creams. However, if it does not work then consult a doctor instead of doing experiments on your skin.
If your bump is getting worse then may be home remedies will not yield desired results. You better contact a dermatologist as it may require surgical removal.