Product "A", Product "B", and Product "C" are all products in Product Bundle "ABC".
I'm trying to achieve the following scenario:
If a user is on the product page for any individual Product, a link will be displayed that sends them to the Product Bundle page.
If there is a way to do this programmatically so that this will apply to any and all bundled products, that'd be great (i.e. Products A,B,C link to Bundle ABC, Products D,E,F link to Bundle DEF, etc.)
That is definitely possible. This Magento Stack Exchange post has code that could be a reference to build the custom function you are looking for:
Take into account that is an old post, and the version for that solution is Magento 1.7. Still, it's a good starting point to build the solution.
Is the reason for wanting to do this because the customer should only ever view these products as the bundle and not the simple bundle products? If so, why not just set the simple products are not being visible individually? If the site is already live and has traffic going to the simple product URLs then you'd need to set up some redirects but any new products wouldn't be affected as the new simple products would not be show as individual pages.