Is there any way of hiding this on our store so that customers can only view with an upsell?

Hide Bundle from catalog page

If you create a Bundle with discount type, you can hide it from the catalog page ("all products" page) by creating a collection called "All" that will replace the default Catalog page, and then you can make this collection smart (automatic collection) by adding a rule "If Product Type is not Bundle". This should add all products to this catalog page except the Bundle.

Hide Bundle from search results

Then, to hide it from the search results, you can try to tag this product, for example tag it "hide-product"
then, inside search.liquid file, add something like in bold below

{% for item in search.results %}

{% unless item.tags contains 'hide-product' %}
% endunless %}

{% endfor %}