Translation:The woman eats the salt, I drink the milk.
Because "the milk" is the direct object of "drink" and it's definite (because of the "the") -- and definite direct objects take the accusative case in Turkish, which is -i (+ vowel harmony).
So as you turned tuz into tuzu (because it's definite, "the salt", and the direct object of "yer"), you have to turn süt into sütü.
I'd say when it's an active sentence 'bir' is necessary because otherwise it would sound very colloquial to omit it. If it's a passive sentence 'bir' is optional though.
Edit: In active sentences if you stress on the subject and the subject comes right before the verb since it's stressed you can omit bir but it still sounds colloquial.
Sonra turist geldi. -> Then a tourist came.