Is it permissible to give last year's zakat, from Ramadan until now, to a public bathhouse?

It is not permissible to delay Zakat (definition) beyond its due time. Whoever delays it must offer sincere repentance and promptly disburse it to those who are eligible, who are the eight categories mentioned in the verse from Surat At-Tawbah (definition): "Indeed, [prescribed] charities are only for the poor and the needy, and those employed to collect [Zakat], and for bringing hearts together [for Islam], and for freeing captives [or slaves], and for those in debt, and for the cause of Allah, and for the [stranded] traveler - an obligation [imposed] by Allah. And Allah is Knowing and Wise." It is not sufficient to give it to pigeons or to anyone other than these specified categories.