Instead, the "double entry" that complements the money leaving Alice's cash ledger is the entry of the value of the book into Alice's "book ledger", one decreases by $20, and the other increases by the same amount.
In an organisation's accounting (Alice LLC), the basis entry would state a debit (increase of expense) in the book expenses account, credit (decrease of asset) in the cash balance. The complete entry would then make a reference to the invoice/receipt of the purchase and the contact details of the bookstore (address, chamber of commerce registration ID, tax number, etc.).
The exact level of detail is determined by how 'complete' your books are supposed to be. A book expense might not mean much to Alice LLC (which does not deal in book sales/purchases), but a laptop should (see more on the subject of fixed asset registries), or a large invoice from a business from a different country (which will require a lot more diligence with tax 'metadata').
On the other hand, the bookstore definitely cares more about books and will then consider the sale and replenishment of its book inventory, and once again introduce more meta-accounting data (see more on the subject of management/manufacturing accounting).
The company's accountant may care about balances and reconciling them back to things like the existence of said book, a receipt for payment or a bank transaction indicating settlement happened. At a big enough company, the accounts payables nerds may come along and be focused on making sure the full process procuring and paying has happened correctly, including record-keeping, tax compliance, and the actual movement of funds.
When you start to scale how all of these processes are executed and recorded, it's dense enough that it still surprises me many years later.