Does everything need a bundle?
Yes a bundle is always, always necessary for entities.

If you don't define your own bundle(s), the entity system will assign a default one with the same name as the entity type for you, and that one will be used.

If you've only got one bundle, and only ever plan to have one bundle, then you don't need to have a specific field in your entity table for it. As you suggest in your question it would always be the same, so would be redundant and just add extra overhead (however tiny) to your db queries.

If you think you might need to distinguish between different sub-types of your entity at some point though, it would be worth building that in right from the start; it really depends on your use case.