take bug report for specific application I am starting android development, and I am looking for a way to get a bug report from a user's phone.

I know about the settings / developer options / take bug report system, but from what I have seen, it dumps all logs from all sorts of apps I don't really care about.

Is there a similar method which would generate a similar file, with just logs relevant to my app?

(I also know about adb logcat, which I can then filter on my computer during development, but it's not easy asking users to do that!)
You should try third party libraries such as Android Bug Tracker.  You can find many other on github.