Having more than one book seller appraise or bid on your library is absolutely acceptable. Just as getting several opinions of the value of a piece of jewelry or a painting is good practice, so is getting more than one opinion on the value of a book. There are certainly guidelines that professionals follow when determining the value of a book or library but it is no means an exact science and each bookseller will judge the value slightly differently.

Did the Pennsylvania bookseller give you an appraisal of what he thought the library was worth or did he offer a bid to buy the books from you? If he actually offered to buy the books at a particular price and you agreed to sell then your ethical dilemma is whether you think it’s fair to change your mind and cancel the sale if you find a better offer. If you didn’t actually commit to selling him the books then I don’t see any problem with getting one or more bids. Think of it like an auction, you don’t have to take the first offer you get.