By definition, bursitis means "inflammation of a bursa" (burs - bursa; itis - inflammation of).
Cortisone is a steroidal antiinflammatory medication. It acts by decreasing inflammation. So, injection of a steroid into an inflamed bursa is supposed to help decrease the inflammation in the bursal sac. This, in turn, decreases the swelling and discomfort.
However, a neuroma is a disorder of a nerve. It is usually used to define a tangle or ball of nerve endings that has occurred due to an injury to a peripheral nerve.
When a neuroma develops in a peripheral nerve, the patient may have a burning sensation in the area innervated by the nerve, or a Tinel's sign. The Tinel's is a tingling or electric type of shock sensation when the neuroma is tapped.
While the steroid will not cure or remove a neuroma, it may decrease the symptoms caused by a neuroma.
If you have further questions, you should discuss them with your physician. He/she is in the best position to explain things in relation to your actual disorders. Good luck.