Do I have to print the wrapper to mail the book?  Can I just go to the post office and mail the book there in like a bubble wrapper?

It is not a requirement to print the wrapper. You can simply write the recipients address and your own return address if you like. There is also an option for a single page wrapper that has a predesigned label you can affix to the package if you wanted to save paper. That is the option I choose and I affix the printed label to a mailer.

Thanks!

I think you do need to download the PDF to get the address. The system registers this as "printing". But you do not need a printer.

You don't need to download the PDF, just click on the Print Wrapper button on the transaction on your My Account page then scroll to the bottom of the main blue area of the screen. You'll find a line that says "If you need to hand write the address, [click here]." Do that, and the address comes up in a format that's easy to copy onto your envelope.

However you do it be sure it gets marked mailed though so you can get your credit and it doesn't time out and roll over to the next person.

Here is a link to the Help Center regarding "Getting/Printing the Address to send a Book" and "Can I hand-write the address to a book?".

I have received many books that were mailed with hand-written addresses and have never encountered a problem with these.

PBS did have a study to compare the mailing time for hand written labels vs the bar code printed labels. I don't recall hearing any results. 

Hand written labels that I have received usually have a post office applied sticker with the bar code for my address.