Milk pasteurization in the bottle via water bath: fridge live? I am frequently buying raw milk in bottle, which needs to be boiled for pasteurization. So far I always poured it in a pot, boiled it, and transferred it to a clean bottle after.

Since my old supplier dried up I need to travel a bit to get it, so I am thinking about ways to preserve it a bit longer, preferably 2-4 weeks in the fridge. 

Would it be a good idea to put the glass bottles as they are in a water bath and wait until the milk starts bubbling? This way I won't need to do all the transfers and there won't be any air contact, it would be basically water bath canned. Would it hold for 2-4 weeks this way in my 4C° fridge? Any downsides?

I was also considering pressure canning, but I think this would be over kill for what I am trying to achieve here, which is slightly longer fridge life.
You're in luck!

High-temperature short-time (HTST) pasteurisation for milk can be done at 71.5 °C (160.7 °F) for 15 seconds and extends milk's shelf life to about 2 weeks.  So if you can get a thermometer you don't need to wait for milk to bubble.

It's also possible to use a sous vide method; according to this guide 65°C for 30 minutes. Again, it's very important all the milk reaches this temperature and stays constant during the process. In this case the lower temperature is possible because the exposure time is longer. After 30 minutes, cool it as quickly as possible to 4°C.

To extend the shelf life to ~3 months you need ultra-high-temperature (UHT) pasteurisation (135 °C (275 °F) for 1–2 seconds) but that might be more difficult to control; you need to make sure that all the milk reached the temperature and stay there for that amount of time. I'm not sure this process is possible with home equipment.

Make sure to sterilise your containers prior to adding the milk, to avoid other contaminants.