There is radiation with bone scan, usually, if we are talking of subsequent bone scans, they need to be 6 months apart.
This paper /www.ncbi.nlm.nih.gov/pubmed/27290607
indeed confirms that PET is more sensitive and specific than the bone scan. There, the patients received a bone scan and PET within 3 months. From the conclusion: "Our results indicate that BS in patients who have received PSMA PET for staging only rarely offers additional information; however, prospective studies, including a standardized integrated x-ray computed tomography (SPECT/CT) protocol, should be performed in order to confirm the presented results."
I know this does not answer your dilemma, but perhaps you should consult with a radiation oncologist if you are worried about
the radiation dose. Sometimes, even MRI can be used to put all the puzzle pieces together, with MRI there is no radiation. But, you should know that no scanning method is 100% specific.
Father diagnosed in Jan2011 (at age 68):
DRE positive, PSA 7.5, biopsy Gleason 7 and 8.
Bone scan positive: VL5 and pubic bone
Feb2011: Started hormonal therapy (Trelstar+Casodex)
Feb2012: last Trelstar injection
trimonthly PSA: 0.078, 0.138, 1.08, 1.15, 4.17, 5.71, 4.40, 5.08, 7.08
after 2yrs in the OFF phase and a new spot on sacrum, restarts HT May2014
trimonthly: 0.493, 0.207