Can I prevent my customers from purchasing a product outside of my bundle?

Bundler cannot prevent customers from purchasing bundled products by themselves. Bundler can only prevent customers from receiving bundle discounts if their cart does not meet the bundle requirements.

However, you could try using Bundler together with CartBot. CartBot is used to automatically add configured products to the cart, however the app also has a feature called “Bot works in reverse” which prevents checking out without the products configured within the bot. So, if the same products are configured within the Bundle and CartBot, then customers won't be able to checkout without all  bundled products.