a bloomberg terminal isn't a physical terminal. it just runs on your PC

You need the keyboard and/or B-Unit for second factor authentication. Licenses are for a single person only and not transferable (there are machine-based licenses but those are increasingly rare).

So you need a shipping address.

Don’t a lot of places have a communal / semi-public Terminal? Obviously not for trading, but for information, like a library computer.

Yes, those run on terminal based licenses. Bloomberg still sells those but you need to tell your sells rep exactly why you want one and don't get all features (e.g. IB). They are not very keen on selling those.

I should have specified that you need a shipping address for the ubiquitous keyboard

For an experienced user the keyboard is superfluous and only useful because it has an integrated fingerprint reader for the 2FA - so you don't have to faff around with their flaky "b-unit" hardware token.

(But yes, you at least need a b-unit to get started.)