The bubbles will clear and are of no consequence, they are just gasses that can stay dissolved in the higher pressure of the water piping system but then gas out once the water reaches the lower atmospheric pressure outside the pipes.
Of much more significance is your first question: When is it safe to add fish? No one can answer that except you and the subject of learning how to determine that is often the main topic in our beginner's forum here.
As you may have been told, it is really a positive thing to be able to get mature media (MM) from the filter of a mature tank! Congratulations! But it is important to -verify- that the MM has had a successful "take" in your filter; that it has transferred successfully. Most of the time it does, but there are those few times that it doesn't and you don't want to kill your fish just because of assumptions.
The way you verify things is by "qualifying" the cycling process of the biofilter aspect of your overall filter (the part that involves the beneficial bacteria (A-Bacs and N-Bacs.)) You qualify a biofilter by reaching the last end portion of a fishless cycle (the Fishless Cycling process is described in our Beginners Resource Center at the top of this forum.)) A biofilter is qualified when it can drop a 5ppm concentration of simple household ammonia to zero ppm ammonia and zero ppm nitrite(NO2) within 12 hours of when the ammonia is dosed and repeat this feat for a week without any "blips" of ammonia or nitrite showing up when you test.
When fishless cycling with MM, the process is usually very rapid, sometimes taking only a week (the qualification week) if the amount of MM is large and healthy. The members here are great and will guide you if you don't understand any of this. Most of us use a good liquid reagent based test kit (such as the API Freshwater Master Test Kit or the Salifert tests) to perform the 24 hour (and 12 hour once the process is far along) ammonia and nitrite testing. The members can also help you find the right sort of household ammonia depending on your location.
~~waterdrop~~
