Can I use a custom button instead of a bundle widget?

Yes, you can create your bundle and then use the “Quick Checkout URL” to drive traffic with this bundle directly to Shopify Checkout. 

To do that, simply create a bundle in Bundler app, save it and then scroll to the top of the bundle configuration. In there, click on the “Get quick checkout URL” button. 
Then, a popup will show with the quick checkout URL, which you just copy and use in your custom bundle button in your shop.