Do Advil (ibuprofen) and motrin work as bursitis treatment, or would one usually have to get prescription meds from his doctor?

They may. If you take twice the over the counter dose they may work- that is almost the same as the prescription dose. Ice helps as well.
YES. Bursitis can be treated with anti-inflammatories such as advil (ibuprofen) or motrin. If those do not help, prescription drugs and injections into the joints that have the bursitis may be needed, i will use over the counter anti-inflammatories at maximum dosages first before i become more aggressive in the treatment of bursitis.