I can import .bib records easily, but is there a way to have them linked with corresponding PDFs?
Discussion here suggests that you can export a Calibre catalog as BibTeX
click the arrow next to convert books and create a catalog in bibtex format. ... (you have to select at least 3 [books])
You can then import the BibTeX into Zotero. Whether that transfers PDFs, comments, and tags depends on the ability of Calibre to export that metadata (all of it is supported by BibTeX).
A thread on Zotero forums indicates that Calibre may sometimes assign "silly dates", so you may want to look over your library after import.
I have identified the origin of these silly publication dates (Jan. 1st, year 101): that's the metadata I have in my calibre database for some e-books, probably a default value assigned by calibre when a specific date isn't available in the imported document and designed to stand out when sorted in ascending or descending order.
Alternatively, if you want Zotero to try and find the metadata for your books, you can just drag and drop the PDFs into Zotero and use the Retrieve Metadata function to look up metadata. May even want to combine both approaches and merge duplicates at the end (by selecting the best metadata from both software).