The best way to figure out what these bumps are is to see your primary care doctor
for a history and exam. Depending upon what these bumps look like and where they are positioned, your doctor might want to send you for further imaging or testing. It would be unusual to have bony growths from the vertebrae on the back, but this could be possible. More likely is that these bumps be a benign cyst of some kind, such as a lipoma (a collection of soft tissue just below the skin). It will also be important for your physician to note whether these bumps seem to be pigmented or not (i.e. are they associated with a mole that may be changing shape). A mole that is changing over time is a concern and should be examined by a dermatologist
so it can be safely removed. Depending upon their location, swollen lymph nodes can also cause a palpable "bump", although lymph nodes palpable through the back would most likely be felt near the axilla (armpit area).
I'm sure it is very alarming to have these bumps and not know what they are. Hopefully they are nothing serious, but for your peace of mind and to protect your health, the best thing to do is see a physician for a proper exam right away.