Just to check, we are talking here about Bike rather than TaskPaper ?
(Your screenshot(s ?) don’t seem to include a Bike screen, and the text appears, with those bullets, to be in TaskPaper format)
If that/those screenshots are of material pasted into Notes, then it looks as if indentation is being preserved (each line is more deeply indented than its parent).
Perhaps it is really bullets that you want to add to the clipboard ?
(The Bike editor show structural handles, but Bike text doesn’t per se include bullets)
You may be able to get what you are after, (if that is a bulleted plain text outline in the clipboard) with a script. See, for example:
In Bike:
Copied with the script above, and pasted into macOS Notes:
