The most important note of all is: Do not repot a bonsai until you have informed yourself and weighed all the arguments for and against. There is always 1 week to read, to inquire at a bonsai dealer or to take the tree to a meeting of a bonsai working group to analyze it together. A bonsai tree will stand in a bonsai pot for many years. Except in the case of massive over-fertilization with nutrient salts, we do not know any arguments why a bonsai has to be repotted immediately. There is always time for 1-2 weeks to clarify everything.
Bonsai should not be repotted under the following circumstances:
Don't repot at the wrong time of year. Midsummer is usually not a good time to repot, as is winter.
Bonsai taken from nature (Yamadori) should only be repotted when they have shown significant growth in the previous year.
Do not repot several times a year. Even with very fast-growing tree species, this is by no means necessary.
Don't repot just because 3 years have passed. If the bonsai soil is not well-rooted, but otherwise still ok, you can do without repotting.
A newly acquired bonsai does not necessarily have to be repotted immediately. It is better to first observe the tree for a period of growth and then make a decision.