Do you update the inventory level of the items in a bundle? What about an Offer as a Product?

Yes. You don't have to worry about inventory updates of the items in a bundle. Examples:

Simple Bundles

There are 10 available items of product X and 5 times of product Y.

A bundle offer includes two times of product X and one number of product Y. A customer:

  1. lands on the product page of X,
  2. adds the offer to his/her cart and buys the offer,
  3. the new inventory level of X would be 8 and Y would change to 4.

Offer as a Product

You have created an Offer as a Product named XXY (two X and one Y).

Just like the previous example, the inventory level of X and Y will change from 10 to 8 and 5 to 4 respectively.

Note: An Offer as a Product is a virtual product on your shop that is connected to the items included in it. The inventory level of this virtual product is 0, but you don't have to worry because when someone buys the offer, all the items will be updated.