According to my reading of the bill, the Parliamentary Budget Officer could analyze private members' bills. I did not see his role going as far as assessing the costs or conducting financial analyses of government bills. Having read that, I have a better understanding as to why there are requests for analysis of private members' bills.
Personally, and even as a practitioner of parliamentary procedures, I question the merit of such a provision. After all, the ultimate decision to adopt a bill or not and whether there will be financial implications lies with the Speaker of the House. A situation could arise where an entity of Parliament might decide that a bill contains no pecuniary measures, whereas the Speaker could decide that there were. There could be an internal conflict.
In my opinion, the resources devoted to that would be better used if they served to support members in analyzing the estimates.