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