Here's my question..I got a book sent back from the post office as undeliverable..what usually happens from this point on? I PM the member to see if the address could be changed or whatever as a first step..

Yes, contact the other member to see if the package was returned by error (USPS does this once in a while).  If the member moved or otherwise had an address issue of their own making you should report it to PBS admin.

You can bring it to your Post Office and have them check the address on their computer. If it checks out, they will attempt it a second time without charging you.

Definitely do NOT pay for a second round of postage without getting a credit to do so!

Media mail pricing does NOT include forwarding service, that's possibly why it came back to you, though PO does not have to return it to you without charging you the postage for the return trip (though you don't have to pay it and accept the package back either).