alt Hacker NewsI can't speak for Ireland, but in the UK it is quite common to refer to a Bill (before it has passed) or an Act (when it is passed) with a capital letter, rightly or wrongly, because its name would be capitalised (in this case The Protection of Voice and Image Bill, with Bill replaced by Act once it has become law).
It is also a capitalised term within the text of the law itself.
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I can't find a style guide for the Irish Times, but the Independent's style guide seems to agree with you: capitalize when used as part of the name of a bill or act, and use lowercase thereafter [0]. Perhaps because they are using Bill in the headline as a shorthand for the full-name of the bill (probably for space reasons), they saw fit to capitalize it? Regardless, this is one of those cases where it's not really a grammatical choice but one of style/convention.
[0] https://www.independent.ie/editorial/pdfs/stylebook23.pdf
It also helps that Bill is not a common name here at all (the only Bill I've ever met in my life was an American).
I can imagine how confusing it would be if all instances of the word Bill in articles such as these were replaced with Seán lol.