Try to build a rapport with some of the physicians you see when volunteering. You could parlay that into some shadowing opportunities. The hospital I volunteer in allows a single shadowing shift for volunteers so I'm having to do some legwork.
Being super-friendly with the nurses and techs can be beneficial too. They can introduce you to physicians and recommend doctors who would be receptive to shadowing. Heck, just being super-friendly, hardworking and humble all the time has its benefits. I've been fortunate enough to be allowed stand in on a variety of procedures performed by doctors/NPs/PAs ; intubations, trauma intake, cardiac arrest. I've even helped to clean and suture quite a few wounds too. Most of the other volunteers spend their entire shift standing around, stocking carts and blanket warmers.