Different bundle types have different shipping behaviors:

• Preset bundles shipping rates are based on the parent product only. 
• Fixed-price customizable bundles shipping rates differ depending on whether the order processing is the checkout or recurring order and whether your store uses the new or old methods for processing recurring bundles orders. 
• Dynamically-priced customizable bundles shipping rates use bundle contents to calculate rates for the checkout order and the parent bundle product and bundle contents combined to calculate rates for recurring orders. 

Creating a specific rate for the product that covers the shipping cost regardless of the contents included is recommended. 

Review Setting up shipping for the Shopify Checkout Integration or Setting up shipping for Recharge Checkout on Shopify for more information on configuring the rates.