Line-item veto sounds interesting, but extremely dangerous. Some bills meanings and intent could be completely reversed by vetoing a single provision in e.g. definitions section. This wouldn't fix the bundling issue, it would just make the president another party in it, and give them super-congressman powers with the ability to essentially make legislature all by themselves. (And the first couple of paragraphs on the wikipedia article [1] confirm this.)
You're right about being careful what you wish for. That's half of the reason why I didn't try to present a solution: the problem is conceptually clear, but any specific solution will be muddied by the complexities of reality.
Here's my idea anyway: an independent legislative committee whose purpose is to find bundling in bills and can split/veto/force a rewrite before it can be voted on. A supermajority vote can override it. While we're at it, lets also task it with creating an official name that describes the bill without "cutsie" nicknames that misrepresent the content. But as with most "do it with a committee" solutions, this just pushes the problem down a level. We still need solid definitions for things like "bundled" and "related" and "representative" and a way to evaluate the effectiveness of the committee and to challenge their decisions (supreme court? ugh). So I guess this is less a solution and more just a different way to describe the problem.
Feel free to tear the above apart, but that's kind of the point. I'm glad I'm not the one making laws.
[1]: https://en.wikipedia.org/wiki/Line-item_veto_in_the_United_S...