Does Essential Preorder work with bundles? (Essent Preorder Back in Stock app)

It depends on how the bundle is built.

• Shopify's own Bundles app, and any bundle app that uses Shopify's Bundles API: not compatible. Shopify doesn't allow purchase options such as preorders or subscriptions on these bundles. This is a Shopify limitation, and no preorder app can work around it. Typical signs: the badge shows but the button stays "Add to cart", or the product can't be added to cart.
• Bundle and quantity-break apps that use discount codes: compatible, as long as the items are added to the cart with the Preorder button, not the bundle app's own Add to cart button.

Not sure which kind you have? Ask your bundle app whether it uses the Bundles API or discount codes. Avoid mixing preorder and in-stock items in one bundle.

Shopify combined listings

Add the child products to the campaign, not the parent. The parent can't be bought and has no stock of its own (a Shopify rule), so the app can't change Continue selling when out of stock on it. On themes that swap products when a customer picks another option (like Horizon), the Preorder button follows the swap.

Full guide: Preorder & bundle compatibility.