I am responding to this particular part of your queries first because waiting longer to apply, if that is a practical option (it is not for everyone), is often the best insurance the prospective applicant can buy. Waiting does not guarantee no RQ. But it can lower the risk a lot, and it can also make the process go a lot more smoothly if there is some RQ-related non-routing processing (full blown RQ appears to be limited to the most severely challenged cases these days; there are various lesser RQ-related requests which do not require the applicant to fully document all employment and addresses plus some).
And as someone who waited well over an extra year, I can attest it goes by faster than one might apprehend. Again, if it is a practical option.
In your particular situation, it appears you are talking about credit for three months worth of time in Canada, time in Canada prior to becoming a PR which only gets credit at the half-day rate. So waiting three months longer to apply would cover that period of six months prior to becoming a PR.
And I typically suggest waiting at least a month on top of any period of time for which there is some possibility of an issue.
Which leads to . . .
I do not follow and am not much familiar with the details of temporary resident status. What I do know, however, is that among issues some applicants have encountered, in relying on time in Canada prior to becoming a PR, is the absence of a hard copy visa or permit. That is, I do not know much about what a "bridging work permit" is . . . but for purposes of getting credit for the time actually spent in Canada as a temporary resident, it can make a difference whether IRCC actually issued you a formal visa or permit covering the dates you are seeking credit for. That is, it can be important that IRCC records, your GCMS in particular, specifically shows you had status as a temporary resident during that particular period of time. (Periods in Canada with implied status, for example, tend to be problematic.)
Thus, for example, if you received an actual physical permit from IRCC, as your "bridging permit," covering the dates you remained in Canada, there should be no problem getting credit for that time. Otherwise, it can be a bit more fuzzy. But here again, six months before becoming a PR counts a mere three months toward citizenship, so waiting three months more plus some for a general margin above the minimum would be the safe approach.
Beyond that . . . regarding PROOF . . .
There are many, many other aspects of a citizenship applicant's case which will influence how it goes far, far more than this or that particular detail in proof for this or that period of time.
Many appear to underestimate the extent to which IRCC can sort and figure things out. A decade ago things were different. A lot has changed. The extent to which IRCC can access and research so-called open source information, that alone, now enables IRCC to far better identify applicants with what were, in the past, described as reasons-to-question-residency.
PRs should keep complete and exact records of all international travel. Beyond that, the usual records people keep should suffice.
