Highlight the bulleted items, then on the menu bar, Format > Body which will change from bullet, dashed, or numbered to plain body text.
There is a roundabout way to achieve the asterisk bullets using Text Substitutions. In System Preferences > Keyboard > Text, click the + at the bottom and enter and asterisk in the first column (no space), then asterisk and space in the second column, then hit + again..
Now, in Notes (or any text editing app on your Mac, add an asterisk with no space in front of the first word in the list and a substitution popup will appear, select the substitution and your list will not convert to bullets. If you already have a list formatted as *item (with no space), highlight all lines and right click and chose Substitutions > Replace Text.
Granted, this is a bit of a kludge, but unless or until Apple adds custom format options to allow an asterisk bullet list, it seems the only way. Obviously, someone at Apple thought it was easier to type an asterisk to create a bullet than to change paragraphs to a bullet list. So, it seems to be a hard coded system-wide substitution, good for some, a PITA for others.
Also, be aware the * substitution will occur everywhere (this line was entered asterisk(no space)substitution and the browser auto formatted it with a space without prompting. That can be a problem for abbreviating things like *nix or math functions. However, it can be overcome by editing the spaces out and using arrows to get past the word or string instead of spaces or returns which auto completes substitutions as I did above with *nix.
