I used to have the same problem. And I found the solution :D
Of course, using the "Microsoft Print To PDF" printer resolves the issue for printed document. However, I wanted to "Save (my document) to PDF" so the text is embedded and could be copied.
Also, the "Print to PDF" command cannot be automated using a Macro (or at least I couldn't figure out how), while the "Save to PDF" command is widely documented and allows to predetermine the path and filename using a cell value.
I literally tried everything and I've found a loop hole (by accident).
Like mentioned in the previous comments, all page margins should be set to 0. Also, in the Page Setup > Header/Footer, both "Scale with document" and "Align with page margins" boxes should be checked.
At this point, if you Save to PDF your document, the white bleed lines should still occur in your newly created PDF document.
All you need to do at this point is to print your document using "Microsoft Print To PDF", complete the whole process and your printed/saved document should be OK.
Now, go back using the "Save to PDF" command (either in the menu ribbon or using VBA Macro) and your saved document should be ok.
At least, it worked for me.
I'm using Microsoft Office 2013 on Windows 10.