Milk pasteurization in the bottle via water bath: fridge live?
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.