First of all, describing the glass bottle as being a “milk bottle” will only confuse the issue.
Anyway, I believe your item was made for use in a chemical or medical laboratory.
I’m guessing now, but, me thinks an ingredient(s) are placed in the bottle and then “corked”.
The “corked” bottle would then be placed in the copper base and then either hot water or crushed ice was added to control the temperature of the bottle and its contents.
Then the pump “stem” was put thru the hole in the cork and the lid was “locked” onto the top of the base.
Now the big question is, which you, … susiecat, …. will have to answer, …. is the pump an “air pressure” pump ……. or a “vacuum” pump?
That is important to know as "search" criteria.