One more thing to add to what Peter said, and what you have already concluded: You can't print an A4 PDF to A4 paper if your PDF has crops and bleeds without shrinking it to fit. A shrunken PDF can be useful for general proofing, but not for size proofing. That doesn't mean you shouldn't make an A4 PDF that includes crops and bleeds, but of course the combined size will be larger than A4. The printer will have to print to larger paper, and if you need to give them a real-size printout along with the PDF (which you probably won't, since you will likely be sending it electronically), it will have to be made on larger paper as well.
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