There are two popular bundle building apps that I'd definitely recommend. They have great interfaces and offers a great design portal for your customers when they are building their bundle. Both of these apps should fit your needs.
If there is anything else I can help you with, please let me know.
I have most usually bundle app because this app can manage your inventory with bundle.
I would recommend 2 apps: Bold Bundles and Picky Story. They have great features as you asked for, furthermore, Bold Bundles works well with page builder app like PageFly, so you can have more power to control the design of your product page without coding.
Both have 14day trials and easy setup so let give it a try.
Hope you find this helpful