How correct it is saying: "I don't ever go to work by bus" instead of "I never go to work by bus" Does the meaning of these two questions change?
Both these sentences essentially mean the same thing. If I had to choose, I think the second one is more idiomatic, and probably what I would say.
The first one is ok, but a little open-ended in my opinion. You could potentially follow it up with an exception: I don't ever go to work by bus, but I may try it this week.
The sentence with never is more final to me.
Either sentence is acceptable. However, be aware that the different forms "don't ever" and "never" usually have slightly different connotations. When spoken without emphasis, "never" is a simple statement of fact. To say "I never take the bus," says nothing about why you don't - it might well be that you just like to walk and the distance is short, for instance. To say "I don't ever take the bus", since you have chosen a more cumbersome phrase, suggests that you specifically avoid taking the bus, and that there is some strong motivation on your part for doing so.
Similarly, when using the phrases as part of a prohibition, "Don't (you) ever say that," is a stronger command than "Never say that," and the first suggests that if you do "say that" then the speaker will be personally upset with you.
At least, that's the AmE way I've always heard it used.