The first step to take is to see your physician and ask her whether or not the condition is too serious for you to continue bowling. If she tells you that it is, listen. Also, your doctor may prescribe you certain medications that will help you with your bowler's tendinitis.
Before bowling, try using medicated ointment on the affected area. This will loosen up your muscles, tendons and ligaments and may help you significantly during your bowling.
Half an hour before you're going to bowl, take some over-the-counter pain medication, like aspirin, ibuprofen, or any other similar product. These will help you manage the pain associated with bowling with bowler's tendinitis.
Make sure to wear a brace during your bowling that helps with the area in which the tendinitis is worst.
After bowling, ice the area affected by your tendonitis to minimize swelling and pain. Ice the area twenty minutes at a time, once every 2-3 hours, avoiding direct skin contact with the ice by using a towel or other insulating medium.
About 24 hours after the bowling, switch from icing the tendinitis-affected area to using a heating pad on it. Heat the area for about 30 minutes at a time, once every 4-6 hours.