Could we allow suspended users to bookmark questions? I'm aware that I can't but I would like to have this feature changed.
The technical reason is that bookmarking is casting a vote, and suspended users can't vote. That holds for up- and downvotes, but also voting to delete their own post and bookmarking.
When you're not logged in, you can't bookmark a question either. It's one of the benefits of registering and behaving decently.
As an alternative, you can use your browser to bookmark posts. It has better support for it (in the form of categorization) than Stack Exchange anyway.