How do I charge different delivery rates for different postcodes?

You can set up delivery zones based on postcode or distance to ensure you only offer delivery to certain areas (and can charge based on zone).

This can be configured in Shopify directly (rather than in Bloom). If you go to Settings > Shipping and delivery > Local delivery, you can manage your delivery zones by postcode or radius.

This will take effect in the checkout, and Shopify should conditionally show the "local delivery" option during checkout if they meet the conditions you set up.

You can learn more about these options in the Shopify docs.