I would think you need water in the glass bottle - say 3" in bottom, lay bottle on its side carefully with the water, or sloping so you can get some baking soda in the neck without getting into the water, put straw to bottom sticking out the top even but with a cork plug holding it and sealing the straw and into the bottle, add an empty balloon over the top of the bottle carefully - still horizontal - tie off tight with string etc. Then pick up and gently shake.
Balloon will enlargen with pressure and water level will go up the straw and even into the balloon. It will stabilise somewhere or you may need to do it again with less baking soda!!
Now leave upright for weather to interact. With high pressure, it will try and compress the balloon smaller forcing the water down the straw back into the bottle.
In a Low pressure system, the balloon will relax and expand and the water will rise up. Opposite to what we think perhaps, but it would be a barometer.
Not sure how to do it without the cork or baking soda (Enos would do as well...)
Sounds fun anyway... could be messy too..

Option 2 without the baking soda - place glass bottle in freezer with some water in the bottom standing upright. Let it freeze overnight. (Or empty and add water in the morning with straw, bung and balloon)
Next day, add the straw and also a balloon quickly over the end and seal off - still need the cork plug with straw glued into it (or sealing well against the straw). Don't push the straw and bung in too far yet - just touching the ice so can push it in through the balloon later as it melts (or straight into water if using method 2). Don't hold the bottle with your hands - it will warm it up too soon. OK to touch it once balloon is sealing the end.
This will operate the same as above.
Perhaps I have got this way too complicated - I don't know...