I am uncertain as to what extent people seem to think they have "good bacteria" in their aquarium. What are the qualifications for this "good bacteria" and what are their standards, because what one person may consider "good" the next person may not. You could base this off many factors like healthy fish, clean water, growing plants, breeding fish, etc but... that also varies from person to person, and tank to tank. So in my personal opinion, I don't think those factors should make anyone think they have the best bacteria and healthiest setup for there aquatic friends. Nearly any aquarium can take an unhealthy turn for the worse and vice versa, and some fish and plants can still flourish in not-so-great conditions.
If you want to consider a cycled aquarium as having "good bacteria" I would not state that, I would just say that it is an established aquarium. I also don't find that having an established aquarium has really helped kick start any new aquarium of mine to help it cycle faster...maybe others have had luck with this but adding gravel from an established tank or filtration media did not work for me (although you will find another post on here of a product that did cycle my aquarium rapidly).
So, I hope this post perhaps helps anyone else that is having issues or also struggles with this topic. Keep in mind that this is my personal opinion and what has been my past experience with this issue. I would love to hear others comments and opinions on this topic as well.